Assuming he's a weaker player with the 3bet sizing pre, flop think I'd just check back to pot control. Turn is weird but can't see another option than to call. River you're getting good odds and this could be random button clicking and you block AK and QJ so I'd call and expect to be good often enough to make it profitable

Blockers to AK isn't that good here and he can have JJ, QJ and Tx too. Weaker players often bet merged in these spots and there are not that many possible button clicks you beat so I think I'd just fold river.

Edit: Turn bet was really small so I suppose a call might be better. Weird spot so difficult to solve by intuition.

Blocking AK will be relevant if the major part of his Ax are AK.
Since he is clicking 3bet, I believe his range is very large, unless you have on stats or notes that he is tight 3betting with small sizing.

I'd consider a check back OTF. Your hand is quite protected. Then I like checking it back in order to capitalize on his mistakes. Or do you plan to extract over 3 streets?

As played, I'm folding this ugly river.

I would check back flop and start to bet OTT.

As played instead, I think you can fold OTR. You don't have any read and also he could easily value bet KK+.

Regarding your reasoning with blockers, imho that isn't worth much. I mean, for me, it is just better to analyze some data and infer some solid arguments. It happens way to frequently that we take into account blockers, correctly, but villain ends up having the strong obvious hand you are blocking. Don't you think blocker effect are more relevant against a competent opponent who will bluff at some frequency?

EDIT: In my DB it happens 5% of the times...