Range of hands for Villian is probably a pair of Aces, perhaps with a weak kicker. It seems weird that Villian would check-raise the flop with 2 pair or better, since most players like to wait until the turn to check-raise and collect more money when the size of the bets increase. The fact that Villian checked the turn should have signaled that he probably didn't have anything, but I like your check on the turn in case Villian is setting you up for a check-raise. On the river, Villian again checks. Since he checked both the turn and river, you have to figure that you may have the best hand and should put a bet out there.

What confused me the most about your play was that you only called Villian's raise on the flop. Why not 3-bet with TPTK? If he re-raises, you know he's probably strong hand, but by simply calling, you don't know for sure, thus causing you to play timidly and check down the turn and river.