KK facing river push

[kt421]

The replies have suggested everything from checking the flop, to betting 3/4 pot, to betting the pot on the flop. (Note that all uniformly agree that my bet size of <1/2 pot was poor)

I see the argument for checking behind as controlling the pot size on a board that puts us behind any A and in danger of a flush draw. Checking behind puts the pot at 13.50 on the turn, which costs me less money if I decide to call down small bets and makes it easier to get away if villian makes a bigger bet. But we let the flush draw get a free card. So are we folding to a turn bet when the flush comes in?

Betting the pot might chase out flush draws (though with a villian this loose, I'm not sure of this) and Aces with weaker kickers. Am I assuming correctly that we will fold to any reasonable turn bet when the flush comes in?

It seems, of the two alternatives that include the flush draw hitting on the turn, that checking the flop is the better course? Or does the possibility of taking down the pot on the flop outweigh that consideration?