live 5/10 NL I check-fold KK overpair on flop

[McStinky]

I wanted to post this hand to see if people would call me an idiot or see my point of view. I am reasonably happy with how I played this even though it seemed weird.

I am on the big blind with KK. My stack is around 4000, and most of the stacks on the table are between 2000 and 4000. My image is very tight and solid. Six or so limpers to me and I make it 80. Four people call. Three of them are OK players, one is an aggressive fish.

Flop comes Q74 rainbow. I decide to just check. I figure that if I bet and get action from one of the non-fish, I will have be a little worried. They will be putting me on AQ at worst, and since they limped in it makes AQ and KQ less likely for them. Since the stacks are so deep and the board is so non-drawy, I figure I will wait until the turn to start getting value from my hand. After I check the flop, if the aggressive fish bets I will try to stack him of course.

Everyone checks to the last guy on the button who bets 375 into the 400 pot. He has a stack of about 4000. In a live game this is a really big bet, and big bets in live games usually indicate big hands. Plus, the guy is betting into four people, one of which is a fish who is likely to check-call or even check-raise with lots of stuff and one who is really solid and could be going for a check-raise with AA, KK, or QQ. I conclude that he likes his hand. At this point I put him on 44, 77, 74, less likely Q4, Q7, KQ, or AQ. Other random hands are of course possible too.

The problem now is that because he has position, he will be able to put less money in with the hands that are beat than with the hands that beat me. So the math says that I need to be pretty sure my hand is good at this point to continue. I'm not sure enough so I just go ahead and fold.