I think an interesting way to control this pot is to check this turn and call his continuation bet. If he checks behind you, he's either got a monster or scared pair. If he bets the turn, you flat call, which SHOULD produce one of the following two things on the river: you check, he checks OR you bet, he folds/calls/raises (if he raises, I think you know you're beat).

What could villian have from coldcalling on the button with two more people to act behind him? KT? Doubtful. AJ? Probably. AT? Probably if it was suited. AK? Maybe.

I think if it gets hairy here on the turn or river, I fold. I think my line is the best way to control the pot, but I could be wrong.