I think this is a spot where vilain's range is VERY polarized. After playing this hand, I figured that vilain has a really good spot to bluff !

My 3barelling range doesnt include Jx hands because im likely to cb at some point. I would 3barel sets, AK and maybe the few QTs, T9s in my range. If vilain bluff raise me OTR, I only call with sets (7 combos or 55, JJ and KK), and folding AK and bluffs (AK = 12 combos, bluff = 8 combos). That means that Im folding 20 combos / 27 total combos.. There is clearly a problem with my frequency here.

On the other hand, vilain is very unlikely to call flop and turn with a second pair hand (Jx), so what is this river raise ??? I dont think he will raise worse than trips here and he can only have JJ, 55 and KJ (8 combos) in his range (KK would 3bet pre). Im not sure if I should call AK here to have a better calling frequency OTR because I dont see what bluff vilain can have for raising, but at the same time, there is only few value combo in his range..

1) would you bet this river to get value from KQ, KT type hands ? or you prefere checking back ?
2) if you do bet the river, do you call or fold with AK when vilain raises ?

Thx