5/10NL KK vs ?? tough spot?

[PokerForMath]

I have 1350 in front of me, on the button. I have VPIP=22 and PFR of about 17. I have been playing very aggressive.

A LAG play pots it from utg+1. Folded to me, I 3-bet making it 120. I have been doing this a lot, so it does not necessarily mean I have anything at all. The bb is a TAG player with a PFR % of < 10. He 4-bets me to 400. I get a bit suspicious that he might have AA, but it's hard to laydown b/c I have been 3-betting so much that I could see this as 99-QQ, AK as well, though on the other hand he is really tight so I am not sure.

I decide to call. The flop comes 236 rainbow. He checks. I decide to check (mistake?). The turn comes another 2. There is 840 in the pot and he bets 500. I have 950 left. What do you do?