4betting KQ here is fine if they are 3betting you a ton, expecting them to fold quite a lot.

Flop I'd bet when they check, don't think they have us beat as they would be betting all value hands, turn is bleh, if they are 3betting you a lot, no reason why they can't have almost every Ax in their range.

Turn we only beat a total bluff that gave up on the flop but decided to bet the turn, which does not make that much sense as they would bluff the flop. Would sign fold as I expect them to have Ax or better.

A 4b is likely +EV here but I don't see it being more profitable than a flat IP vs a range you are likely ahead of.

Not sure why you checked the flop - we should be looking to get it in over 3 streets on a lot of runouts so clear Vbet. I might choose to bet 100% of my range largely because it doesn't seem like villains are protecting their checking ranges enough at these stakes and there's a lot of value in the protection you get with your weaker pairs.

OTT folding might be exploitatively fine if you decide that villain always has SDV when he checks the flop. calling is also fine I think but never great as you might just be behind 100% depending on what villain is doing and you can expect to get bluffed OTR sometimes so readless it's tough to see this being super-profitable.

Thanks guys, flop check/back is just stupid... Bet bet bet!