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Hmm... I'm not 100% convinced you're up against AK here. You could as easily be up against AQ or even QQ or JJ or something. With a marginal hand, it makes sense to check-call, check-fold in first position and if the villain doesn't bet the turn, to fire at the river.
I probably would have bet that turn, defining his hand. If he didn't have an ace there, there's a good chance he'd lay it down. After all, you have a full house that only loses to one hand (and a very unlikely hand at that - there are 2 kings and 1 ace out there already, so there are only 6 rather than 16 permutations of AK left). He might think he's "trapping" you with KQs, or the K might have scared him if he had AQ.
On the river, though, great fold. Nobody is going to fire into that pot without an A or a K. You've got to give up there.
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