TPTK in bvb vs nit-reg

Villain is a reg but limp/calls that's often a pp. b/b/b is a good line with tptk. your turn c/c is good too since he folds to alot of barrels and rarely has a worse ace with the preflop action. i like a b/f on the river of maybe 7-8. you could get a suspicious call from a fairly wide range. c/shove doesn't sound right, he shouldn't have any AQ or AJ hands.

Edit:
I misread the hand, sorry. Villain didn't limp/call but over-called in the big blind. So check/shove is reasonable, he could have worse aces. But I still like a river b/f since I doubt he b/c's worse but he could check behind with worse that might call a bet. If you were gonna check/shove, you should probably do it on the turn.