KK: 4-bet pot A high Flop

Just my thoughts; I am not an advanced player by any means!

I don't think he needs to have a great hand to 3-bet you from the BB, because he might suspect you simply of stealing. Calling your 4-bet is obviously a bit more worrying!

I think I would like to c-bet that flop and see where I am. If he calls, maybe I shut down on the turn, and go to check-fold. It would depend on the opponent. I think your check behind him signals that you don't have the A and encourages him to bet the turn. I agree he's giving you great odds, though, so I guess you have to call in that spot. His check on the river is a bit suspicious - surely he would bet for value if he thought he were ahead, unless he hoped for a bet from you that he could check-raise.

I am sticking my neck out here and possibly going to look foolish! Did he have something like JT?

I would most likely 4bet a little bit smaller in position. 40c is big enough I think. The rest of the hand seems fine to me to check the flop. I expect you get only action of better if you bet and now you give him the opportunity to bluff sometimes on the turn.

Cheers,
SDK1987