River betting confusion

[natarish]

Blinds 100-200 and antes 25. 10 Handed Table.
This Hand came up during recent LIVE mtt.

Villian is very Nitty player. His open raise range from UTG+1: JJ+, AQs+,AKo

Villian open raise for 500 and it folds around to Hero in BB and calls the extra 300.

Hero (BB): 10500
Villian (UTG+1): 20000

Hero: :3c :5c


FLOP: :3s 4c :5s
POT SIZE: 1350

Hero chks, Villian Bets 700 and Hero raises to 1.6K, villian calls.
i decided to chk-raise to represent draw heavy range from blinds and my small amount of raise also represents a cheap bluff on scary board that misses Villian entirely.



TURN: :2s
POT SIZE: 4350 Hero: 8.4K Villian: 17.5K

Hero Bets out 2400 and Villian instant calls. i bet small to get villian to shove light, but there are no unpaired hand in his range with backdoor flush draw that would shove here light. So i really disliked my turn bet amount.



River: :7d
POT SIZE: 9150 Hero: 6K Villian: 15K

Hero shoves rest of his stack, Villian tanks for almost 3-5mins and calls.

Here is the real issue for me. I have narrowed down his range to
AsJs+(nut flush), JJ,QQ,KK,AA


Real ISSUE for me is figuring out what part of his range has JJ, QQ,KK and if his range is largely made of JJ-KK pair hands then i should shove for value.


So if i shove the river: villian calls with JJ+, AsJs+
If i check: Villian checks behind with JJ+, but shoves AsJs (nut flush).
Villians bluffing frequency with busted draws or random unpaired hands is very low.