Hero didnt think before checking the flop. You cannot rep anything now and when you c/c flop, this villain will know whats going on. We wont stack this villain if he has JJ TT IMO.
bet bet bet setting up a perfect rivershove bet size is the only way to play a rainbow flop vs a decent hand reader. It keeps our range this widest.
The only thing now that you could do is tank and do your best acting job to convince villain you have AK and dont want to lay it down. I would call flop now, and chk turn, and chk river if villain checks back turn.