I don't think you did anything wrong here. If he's check folding you were probably never getting anything out of this hand. Even if villain hits a card on the river it'll probably not give them anything that they're going to call or bet big with. They might have bluffed the river but then again maybe not.
On a turn like this there are a lot of hands (draws, pairs, low two pairs) that villain could have that would happily call but might prefer to check if they can. Betting will get more value out of these hands than slow playing in my opinion. I'd probably bet big on this turn, about third pot, to get value from these hands and just accept that villain is folding a lot of the time. The fact that you didn't three bet also means villain might discount you holding AK making it more likely they'd call.
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