Hizbullah / Hezbollah (just the group)

[Rex Brynen]

Iran doesn't have much capacity to smuggle substantial ATGM capacity to Hamas in Gaza, and almost no capacity to get anything into the West Bank. The most you find is a few RPGs (usually with regular, non-tandem warheads) and IEDs/mines, and in Gaza only. Given how casualty-averse the IDF is, however, that's a substantial deterrent.

Regarding Iraq, its almost inevitable that Iran will, in the long term, be providing some security assistance to Iraq--indeed, Ahmadinejad has made the offer. Indeed, some (now senior) Supreme Council military cadres held IRGC commissions during their exile in Iran in the 1980s.

[Rank amateur]

I'm just speculating that Iran could get more aggressive once they have a nuclear bomb, or if we get aggressive with them, but your points are well taken.