Israel responds by targeting Hezbollah weapons, assets and militants.
That doesn't explain why the average Sunni Lebanese in Beirut would feel like they need to "resist" Israel.
Certainly Israel's invasion of Lebanon in the early 80s affected many inhabitants of Lebanon, not just palestinians.
The average Sunni Muslim in Beirut either remembers, or has family who remembers what happened during the (unprovoked by the Lebanese) Israeli invasion and subsequent occupation. Today, most of the Arab world supports Hamas in the Gaza war, considering that the large number of civilians being killed is essentially mass murder. Mix these two informations, and you will find very little trust towards Israelis. Add today’s attacks and things get even worse.
It’s very easy to destroy trust, and very hard to build it. None of this has to be perfectly logical - it’s not how people work.
(94)Chapter: Fighting against the Jews Sahih al-Bukhari 2926 Book 56, Hadith 139
(Part of Sunni Islam)
Actually they were conceived and rose to prominence in direct response to this rather substantial provocation:
The occupation came as a result of continued attacks. And after Israel left in 2000, more and more attacks happened, culminating in the 2006 war.
The fact remains that if no there were no threats against Israel from Lebanon, there would be nothing for Lebanon to fear from Israel. It's repeatedly sought and made peace with every sovereign country with which is has no ongoing disputes.
(There are, as I understand it, some minor territorial disputes along the border. I'm sure these can be quickly resolved through negotiation, if all parties are serious about it.)