While i'm reading the post i'm thinking c-bet the flop, but you posted the result and now i'm a bit biased, can't think properly. I think if you put him on a big hand on the flop (i'm guessing this since you decided to check), you bet he raises and you can fold (I probably wouldn't but i'm working on toning down the stubborness).
How has this player been playing up until now ? He played tricky with that AK, maybe hoping for a multiway pot but I doubt it, must be a fish.
Against a regular fish, I would c-bet the flop, fold to a big raise (TT, JT, QT, QJ, AK, K9), (but also AQ, AJ, AT, KQ, not to mention KT, Q9, Q8, Q7, ...).
I'm not sure but playing the hand like you did, i'm just calling the river (take the minbet like a check), like to see better players opinions though.