I really think you should bet this flop. Even if you give him such a narrow range as KK-JJ, you will lose alot of value if you check-call like this. You will get a call from both JJ and KK if you bet something like 2/3 pot on the flop. You will also probably get his KK all-in on the turn if you follow up with another bet.

However, I think you give him way too narrow a range of hands. You will get called by lots of lesser hands, such as 99, TT, AK, AQ. If you add these hands, I think you should be even more inclined to bet.

Dumle