I would've played this exactly the same way you did.

Someone mentioned a c/r on the turn to trap the SB. But I'd save that play for a dryer board than this. If SB called the 2 bets on the flop, he's likely on a draw and you leading the turn could've priced him out.

I think you're ahead most of the time here. Most players would reraise QQ preflop, so I think that's less of a possibility than TT. QT is entirely possible, I see morons cold calling QT all the time. 44 is statistically less likely, but possible. I'd also include KQ and AQ in villian's range.

I wouldn't go for a 3bet on the turn or river. Villian has pumped every chance he's had, I'd give that some respect.