[bobdibble]

Unless he is making level 4 move on you, he can beat a J, and probably can beat a Q.

His flop lead looks like it was begging for a chance to 3-bet considering you capped pre-flop.

On the river he knows that if you were drawing, you will fold. If you have 1 pair, you will call if he bets. But, if he checks, you will value bet your pair, giving him the chance to CR. He is saying he at least has an overpair, and maybe better.

Now, there is the off chance that if he believes you are playing your A+ game that he knows that this will be your thought process. So, he could CR with his busted AKs nut flush draw or something similar as a level 4 bluff if he believes you are playing well enough to fold a J or Q to this move.

My guess is that this is the more basic scenario though, and you should have folded.