I don't like the turn bet, I not expecting any pair (or PP) to fold on the turn K, I do expect all worse hands than ours too fold though. I would check it back and get to show down. If you're going to bet on a K turn, I'd rather we bet the flop than check and bet the turn as we rep very little.

Why did you bet turn after the first check? You showed weakness then, so you could expect a turn raise.

Pre: I like three betting here. I don't hate a call but three betting is definitely superior IMO.

Flop: I like checking this back here. AJ will have some showdown value for sure and we are not likely to fold out many better hands with a single bet so if we are betting flop we will probably have to continue barreling here to turn a profit which I am not a fan of doing in a blind vs blind war.

Turn: I see no reason to bet here, again we have showdown value and we are never folding out better on this turn so betting here seems bad to me. When we do bet and get raised I fold it, as mentioned though I would far prefer to not have put ourselves in this spot in the first place.

River: If we played it as I suggested on the turn then I would be checking back/calling a river bet from villain. As played, I would be folding to a river bet and checking back when checked to.

3 bet pre is standard for me, and I like the check back on the flop with nothing really going for us on this board.

On the turn I'm torn between betting really small and checking. If we expect to have the best hand a decent amount then in effect it's betting for protection and we stand a chance of villain not realising some equity on the river. We also prevent ourselves from getting bluffed on the river which is worth some EV at least.

A lot of the time we can check back on the flop intending to bluff turn and river if villain checks to us twice, but when the turn pairs the board it's tough to rep much. Although we should be capable of checking back some weak Kx and QQ JJ TT on the flop which can now legitimately bet for value, I don't think we ever get a lot of credit and are kind of committed to bluffing the river if we take this line.

If we check the turn back and face a bet on the river at these stakes I'm really not happy about bluff catching as I would expect villain to take his chance on the turn rather than the river.