Is there any way to get away from this?

3/5 NL Commerce. TT in EP. I make it 20 to go. 3 Callers including villain directly to my left. Pot ~80 Flop is unsuited rags. I bet 40. Two call. Pot now 200. Turn is T. I bet 100. Only villain calls. Villain is a tight-passive old guy that I've played against several times. Calling the 100 means for a fact that he has an overpair. Most likely aces or kings but QQ and JJ are possible. River is (GOD DAMMIT!) an Ace. I close my eyes and push all in for another 200. He calls and shows me his AA. Now there is no way my money isn't going into the middle here if villain bets, but is it better to check the river so that I have a better chance of getting action from JJ-KK? Or does JJ-KK call enough/check behind enough to make the all-in bet the proper play?

Yes I should have made a pot sized bet on the turn because I still get action from an overpair, but since I didn't what is the best play?