Preflop is fine I think, at our limits. Pot size is 17c which is only 2c more, so meh.

Postflop, I think you are overplaying your hand. AK has bags of showdown value and you have hands that want to check (as you pointed out) so you need some oomphh in your checking range or you are folding turn too often when you check. AK with K hearts fits that well, I think. Thinking about villain's range overall on the flop and turn you are behind at least QQ, JJ, 99, JX, AhXh, XhYh plus anything else he gets sticky with like TT. A check on flop would allow a call on the turn with your Kh and you could fold the river if Villain still bets.

Given you bet flop, on the turn you also need some checks and I think by betting this hand ( and others like it) you are now too wide on the river when Villain calls turn. So you have to fold a lot of hands to his river bet which is why it is an easy fold.

wp