KK played very weak

My thought after the flop came was this:

What hand calls a $2 raise preflop, checks and then calls my flop bet.

It felt a lot like a pocket pair to me, which may have hit the set. Of course, I suppose there was always the chance that he was initially holding something like 99,TT,JJ.

How many people here with just 2 broadways will call a $4 bet there?

...hmmmm