Why are you checking the turn here? (Except for to induce a river bluff) The two is a pretty decent card for you, It's fairly obvious you have overs and would call a turn bet if Villain bet - maybe he was hoping for a c/r....

I think the best line is b/f the turn though as he's not very aggressive and probably would just flat call all over pairs and rase the trips/boat. You can discount AA/KK, so you're ahead a lot here, just A2 44 and 55 that have got you. I think they mainly bet this turn though esp 44 and 55.

As played you have to call the river, nh