That is a very tough flop for your hand. I don't see you ahead much, don't see him folding a bunch either. You are really only ahead of QJ, KJ, maybe good SCs. Best I think is to b/f that flop. As played, that river is also very tough, either he's got it or doesn't (that is, Ax or good PP), think that's a fold too.

PS: excellent hand for analysis OP, very interesting hand, would like to see what others say about this.

He win and show me A9o.

I don't think we can call this pre. We are to often dominated...

as played I would b/f the flop...

OP: the way villain played, it really looked like an Ax...

thia: I understand what you are saying but I'm not folding KT to a 3bet, even a big one like this, I think there's a lot of value from (1) hitting and (2) villain misplaying postflop to fold KT in this spot. Remember, there is so much horrible play postflop in 3bet pots, learn to master this spot and you are ahead of most, and hands like KT are at the bottom end of my big 3bet calling range.

Fold preflop to a reraise.
As played bet flop fold to a shove or reraise.

meh...KTo is kinda on the loose side imo...maybe KTs so we have some extra equity...