A range does not consist of one hand. - Like carrot said, AK is a very small part of his range there, especially after he flats pre IP.
So you understand that you mostly beat bluffs and thin value raises on the flop, right?
So the K is a scare card if anything, and if he was bluffing, it's a great card for him to continue to represent. Check is fine, but C/R I don't get at all. You're basically hoping he hit a K, AND is going to stack off with it.