River range bet sizing?

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River range bet sizing?

BN: $1415.70
SB: $1005
BB: $2160.16 (Hero)
CO: $1023.50
Preflop ($15.00) (4 Players)
Hero was dealt 6 6
CO raises to $22.79, BN folds, SB folds, Hero calls $12.79
Flop ($50.58) 6 2 Q (2 Players)
Hero checks, CO bets $28.96, Hero calls $28.96
Mixing it up between c/r and c/c.
I want to be able to c/r some FDs because I can't call again on most turns, so I need to keep sets in my flop c/c range.
Turn ($108.50) 6 2 Q 3 (2 Players)
Hero checks, CO bets $77.04, Hero raises to $238.85, CO calls $161.81
Maybe a little too small
River ($586.20) 6 2 Q 3 5 (2 Players)
Hero checks

So should we have a small betting range on this river, or split our range into jams and checks?
My main turn c/r bluff is spades, so nothing missed on the river.

Because I'm not bluffing, perhaps I should bet 1/4 pot with sets and flushes? But that strategy really hurts the EV of not jamming flushes.

I do think that betting 1/4 pot with my whole range is tough to play against, and it will be hard for him to bluffjam, whereas a check gives away more information on my range.

Thoughts?

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