[olliejen]

First, I don't think this is AA, b/c I think it's pretty standard for this type of player to repop you pre-flop. I generally don't think we can discount KK or QQ at all.

About say, 15 ways you are crushed.

I think it's possible he plays TT this way, and there's one combination of A[img]/images/graemlins/spade.gif[/img]K[img]/images/graemlins/spade.gif[/img] and JJ.

So about 8 ways you are way ahead (edit: you're only way ahead of TT, but I'd say you have significant equity edge vs AKs on the turn and fold equity vs the other JJ)

Barring more info, I generally don't think button calls your pre-flop 3-bet with pairs 99-22.

I think you really need to bet this flop in order to give him a chance to fold out hands that crush you (not likely, but possible; if he's got QQ or sometimes KK, you'd be playing AA the exact same way). Also, if you bet, UTG+1 comes along, and Button is still calling, the pot's protected at that point. There aren't many hands he can call w/ impugnity.

By check-calling, you're in a weird spot w/ the stack/pot ratios and no real idea of where you stand in the hand.

Just based on the Bayes, it seems almost twice as likely you're losing here than you're winning. I would check and fold to a bet. if he checks behind, I'd bet probably most rivers.