I think we bet with the best hand on the river, if you plan to turn your hand into a bluff, do it on the turn when the ace hit not the 7.

I'd check this down on the river as I don't see worse ever calling.

Hard to tell if your river bet was for thin value against Kx or a bluff.

Being OOP sucks.

Harvie suggested betting the A on the turn, I am not so sure about this line as we will never fold out Ax ourselves and I would guess pretty much every other pair that beats us will call at least one street here in position so we are spewing chips I think by betting here.

On the river the same logic applies, I would expect very few hands that have us beat to fold here so all we are trying to do is to extract some very thin value from Kx which is a bad plan IMO. I would be looking to check this down and expecting to be good here somewhat often.

I don't mind double barreling once villain checks the flop. He's going to have Ax some % but from MP he's going to c bet those combos some of the time too.

Facing a bet on the river I would expect him to be able to fold 8x and small pocket pairs which beat us. We also gain some protection from getting bluffed by missed draws he decided not to c bet.