River bet-sizing in 3b pots as preflop caller

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River bet-sizing in 3b pots as preflop caller

BN: $458.77 (Hero)
SB: $150.20
BB: $493.02
UTG: $275.10
HJ: $708.70
CO: $97.12
Preflop ($3.00) (6 Players)
Hero was dealt 7 6 4 Q
UTG folds, HJ folds, CO folds, Hero raises to $4, SB folds, BB raises to $13, Hero calls $9
Flop ($29.00) 4 J K (2 Players)
BB bets $16, Hero calls $16
Turn ($61.00) 4 J K 6 (2 Players)
BB bets $36, Hero calls $36
River ($133.00) 4 J K 6 5 (2 Players)
BB checks
Assuming preflop, flop and turn is fine, and assuming that I should bet - how do I size river VB here? On one hand I would like to size smallish so his calling range is 1P heavy (OP etc). But by betting bigger I polarize my range inducing more hero calls. So in a vacuum, which size completes the purpose best?

Also; how should I categorize my ranges here? I have VB hands (where 2p is in the low end obv), I have nuts and I have a lot of air. Should I have a one size fits all; i mean bet my entire range the same amount? If so; should chose the sizing based on my overall VB/bluff ratio here? And what if I have more AIR than VB hands here, should I then bet small instead of big because I am never bluffing?

Please enlighten me, I have been struggling with this for several years, never really coming to a conclusion.

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