I would c-bet the flop for value here. BB may be unknown, but you'll still be taking the pot down lots IP here or you could be called by worse hands including draws and worse Ks. I like to keep initiative and chbk most turns to pot control. When you don't cbet, you're likely to be lost facing aggression on non-J turns/rivers.

As played, defo calling the turn. He could be stabbing here with loads of draws and Ax which you've got crushed. Probably calling most river bets as well.