[fluff]

I'd cap the PF. KK is a great hand to have heads up.

Flop brings a scare card, but betting out is ok.

I don't understand the turn check raise. Do you think it was for value or trying to push him out? Either way, since he doesn't drop out, you have to figure him for having an A. Along with PF 3-bet I'd put him on AQ or AK. Unless you read him as someone who is insensitive to PF raises and someone who falls in love with QQ or JJ, you're likely behind here.

After your check raise got called on the turn, I'd check-call the river, hoping that he'd check behind you.