The play is extremely weired since there arent any draws out there. Villain should know that you hold either KQ,KK,AK or AA considering you raised pfr and 3bets the flop. So if he has a hand that beats that he should bet cause he knows you will call. When he doesnt bet turn he shows weakness and a river bet is in order. Hopefully he will call and show you something wierd as QQ. If he raises I think you can very safely throw your hand away.

Ps. This is if he isnt a total maniac. Then you should bet call.