[Nick C]

On the flop, there's not much Button could be raising with (unless he's simply bluffing, or he thinks you are) except a king, a pocket pair, or a six. Of those possibilities, I think a king is most likely.

When the second king falls on the turn, I start thinking there's a really good chance I'm in trouble (even though it did just become mathematically less likely than before that Button has a king). I find it hard to fold a boat, but I think I'd go into check-call mode here. In any event, if I did bet, I wouldn't 3-bet after Button raised.

On the river, I don't see much point to betting or checkraising. Even if Button can't beat the board either, I doubt he'll fold.