Saudi Arabia has started to change its long-held policy of supporting Lebanon.
The US has been pressing the Saudis to continue their traditional support to Lebanon. Were it not for this US pressure, the Saudis would probably have gone further in their new measures.
Hizbullah has been for a long time part of the Lebanese government. The Saudis never thought before of imposing sanctions on Lebanon for that reason.
It is true that the US (and European countries) were always encouraging the Saudis to support Lebanon (and this is no doubt an important reason for the traditional Saudi support of Lebanon), but the Saudis themselves were comfortable spending money in that country. Even in the 1990’s when they had a financial crisis they kept spending money there.
Lebanon is not a developed country. It is in fact one of the most undeveloped countries in the Middle East. The infrastructure there is horrible even in the standards of the Middle East, and the Lebanese government is very unstable. When this government exists at all, it nearly always has other concerns than looking into developing the country. This is basically a country without a real government, and without a government you cannot have a real economy. The Lebanese people rely on two main financial sources for their subsistence: tourism and expat remittances. Because a big part of tourism and expat remittances comes from the Saudis (and their GCC allies), the Saudis can devastate the Lebanese economy if they wish to.
But the Saudis never thought of doing something like that before. For them (and for others in the region) Lebanon was a useful playground. Because Lebanon is located between Syria and Israel, gaining influence in Lebanon could enable you to harm either Syria or Israel if you had an issue with one of them. Some regional players (e.g. the Islamic Republic of Iran) used the Lebanese playground to harm Israel (e.g. via Hizbullah), while others used it to harm Syria (e.g. Saddam Hussein).
Perhaps all the Middle Eastern powers tried to harm Israel at one time or another. This is traditionally an easy way to gain popularity in the region, because Israel is deeply hated by the peoples of the Middle East (save the Israelis themselves, of course). Before the recent war in Syria, Iran had gained popularity among many Sunni Arabs for its efforts against Israel.
However, the Saudis never tried to harm Israel from Lebanon.
The Saudis traditionally are not considered among the big powers of the Middle East. It is perhaps only in the last decade that Saudi Arabia suddenly emerged as a huge regional power. Saudi Arabia was formerly a vulnerable country whose fate largely depended on American support and protection. Its situation was similar to that of Israel. For the Saudis, the perceived threat of countries such as Egypt under Nasser, Iraq under Saddam Hussein (particularly after the invasion of Kuwait in 1990), and Iran after the Islamic Revolution was a more important concern that trying to gain influence in the region by challenging Israel (while Israel is an oppressive country against the Palestinians, it has not in a long time shown any expansionary ambitions).
For the Saudis, intervention in Lebanon was not a way to gain regional influence, but a way to prevent other countries from gaining regional influence by challenging Israel from Lebanon. This is a hallmark of Saudi policy in general. The Saudis always seek to preserve the status quo in the region. They fear change. This partly has to do with their nature as a very conservative people, but it also has to do with a realistic fear over the fate of their regime. The Saudi political system is a very primitive political system, and the House of Saud are not mistaken when they think that this system may collapse under pressure from a big regional power.
Before the attacks of 9/11, the US never sought to change the Saudi political system or even influence that system. Even after the attacks the US did not push hard for reforms in Saudi Arabia (although there have been some reforms, to be fair). This is why the US is a very trusted ally of the House of Saud, and why the Saudis work ardently to preserve American hegemony over the Middle East. They see American hegemony as a guarantee for the future of their rule.
Because of their opposition to Nasser, Saddam Hussein, Hamas, Hizbullah, Iran, etc., the Saudis can appear as friends of Israel, but this would be a false perception. I am sure that the Saudis (like all Arab countries) will be happy to become friends with Israel after the Palestinian issue is resolved, but to think that the Saudis will abandon the Palestinian cause and adopt the US position on Israel is wishful thinking. For the Saudis, Israel is the least concern in the region, but it is still a concern.
So basically, Saudi Arabia does not want to confront Israel because it has more important concerns. The Saudi intervention in Lebanon is traditionally not aimed at pressuring Israel but at supporting a strong Lebanese government on the model of the Syrian government, that is, a government that uses strong rhetoric against Israel but does nothing in reality to annoy Israel. A country ruled by such a government would act as a buffer zone protecting Israel from countries that actually want to pressure Israel (most notably Iran). This is why the Saudis collaborated with Hafez Assad in reaching the Ṭāif Accord which ended the Civil War in Lebanon. That accord made Lebanon a puppet state in the hands of Assad. That was not seen a big problem, because Assad was not seen as a real threat to Israel or anybody else in the region.
Things got out of control in Lebanon after little Assad withdrew his troops from the country in 2005 (under international pressure). After the Syrian withdrawal, Hizbullah filled in the vacuum and became the dominant power in Lebanon, which practically meant that Lebanon was in the hands of Iran (Hizbullah is an organization that takes direct orders from the Supreme Leader of Iran, and they do not hide that). Now you got a real enemy of Israel in control of Lebanon, which is exactly what the Saudis wanted to avoid since their intervention in Lebanon started in the 1980’s.
When Hizbullah attacked Israel in 2006 the Saudis publicly condemned Hizbullah. That was unprecedented in the history of the region. Traditionally when somebody fights Israel everybody in Middle East support them, at least verbally. That showed why the Saudis really hated Hizbullah and Iran’s control of Lebanon. The Saudis believed that wars between Hizbullah and Israel would enhance Iran’s position in the region. For one thing, such wars will convince the people of the region that Iran’s ‘Axis of Resistance’ is a real threat to Israel and nothing like the rhetorical ‘resistance’ of Syria. If they become convinced with that, Iran will inevitably gain a huge popularity. Eventually the US will have to force concessions on Israel in order to settle the Palestinian question and end the dispute with Iran and its allies. For the Saudis, such a scenario would be sinister, because if concessions can be forced on Israel, they can also be forced on Saudi Arabia.
The Saudis would not want to grant concessions to the Shia minority in their country, because such concessions go against their political philosophy. Besides, if the House of Saud grant concessions to the Shia dissidents, they will have also to grant concessions to other dissents, which means that they will have to do political reform, and this is in particular what they want to avoid at all costs.
The war in Syria weakened Iran’s ‘Axis of Resistance’ and helped the US reach a deal with Iran that does not include any concessions from Israel or Saudi Arabia, yet these two countries are strongly against that deal. They oppose it not because it actually harms them, but because they see in it a bad precedent. They fear that Iran may grow strong again and pressure the US into a new deal, and that deal would put Israel and Saudi Arabia in a position where they will have to grant concessions to the oppressed peoples within their borders (i.e. the Palestinians in the case of Israel, and everybody in the case of Saudi Arabia).
One of the biggest consequences of the war in Syria is that the Damascus government has effectively become a puppet of Iran. Were it not for the generous Iranian support of Assad, he would not have lasted until now. He owes his throne in Damascus to Iran, which is really the only country in the world that sincerely supports him. (The Russians are accused of supporting him, but we read in the media that the Russians actually asked him to resign, and they told the same thing to the Iranians. The Russians do not really support Assad but they are concerned with preserving their influence in the Middle East. If the Russians go into dispute with Assad, that will harm Russian relations with Syria and Iran, which are the only allies of Russia that remain in the Middle East).
In the fall of 2012 Assad cut supplies to Aleppo. That happened just weeks after he effectively withdrew his troops from the city and let most of it fall in the hands of rebels. At that time Assad was starting to draw the borders of what would be later called “useful Syria” (سورية المفيدة). This is the part of Syria which Assad (probably by Iranian advice) found to be defendable, and so he decided to concentrate his troops and resources in it. Although he retreated from Aleppo, he kept pounding the city with bombs to make sure that it would not become a capital of the opposition. (Assad now seeks to lay siege on Aleppo for the same reason: he wants to kill the city so that it does not become an opposition capital. He does not want to retake it, because he cannot.)
The new state (“useful Syria”) which Assad and his Iranian masters drew in southern Syria cannot really live unless the Syrian-Lebanese border is obliterated. This state is not centered in the coast of Syria where the Alawite supporters of Assad concentrate, but it is centered in Damascus. Most of the people in Damascus and around it are not Shia or Alawite and they will not support a new state dominated by Iran. If the Iranians want to keep this state, they will have to rely on support from the many Shia that live across the border in Lebanon. Iran has already involved the Lebanese Shia in the Syrian war by making Hezbollah fight for Assad (Hizbullah in realty is not fighting in Syria for Assad but for the Supreme Leader of Iran. It is ridiculous to think that the Lebanese Shia are sacrificing themselves in Syria for the worthless Assad.)
The Iranian plan for Syria is an expansionist plan, but the Iranians do not seek to annex a part of Syria to their own territory. What they want to do is to annex a part of Syria to the Hizbullah-dominated Lebanon. They particularly want that part of Syria which abuts on Israel, because that part is the most valuable strategically for their ‘Axis of Resistance’ scheme. They want to enlarge the Hizbullah-dominated Lebanon so that it engulfs the entire “Northern Front” of Israel. That will make it easier for Iran to wage future wars on Israel. (Iran has a legitimate Casus belli which is the Israeli occupation of the Syrian Golan).
This Iranian scheme for a Greater Lebanon including Damascus and dominated by Hizbullah is almost a realty. Iran has already laid the foundations for this state. The Saudis see this new reality and they begin to change their traditional policies. For them, it is ridiculous to wage war against Damascus and be friends with Beirut while the two capitals are dominated by the same power, which is Iran.
The Americans perhaps have another perspective. They think that boycotting the Lebanese government will cause this government to collapse, and that would help Iran’s plan to obliterate the border between Beirut and Damascus.