Folding AK when flopping Kxx rainbow?

[Verdi]

I don't have the hand history on this one but it goes something like:

Villain types in the chat: "Are you ready to rumble?"

Villain make a 8BB preflop raise. I call with AK. Everyone else folds.

Flop comes Kxx rainbow. Villain overbets the pot. I call. Turn is a blank. Villain again makes a big bet.

I put him on AA, KK or a lower set and folds. Can I really lay this down at this level ($25NL Party)? Could he have QQ or KQ? Or just nothing at all? Was this too weak from me?

I probably should have reraised the flop to get information from him. But even calling his bet would tell him that I have a good king. How many bluffers will shoot again here on the turn?