Using stats to make a bluff at river against the board?

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Using stats to make a bluff at river against the board?

Blinds: $0.25/$0.50 (6 Players) BB: $100.94
UTG: $196.81
MP: $33.56
CO: $31.08
BN: $50.00 (Hero)
SB: $63.85
Preflop ($0.75) Hero is BN with J T 9 7
2 folds, CO calls $0.50, Hero raises to $2.25, 2 folds, CO calls $1.75
Cutoff is loose-passive fish, with tendencies that make it profitable to play against him in position. His check-raise is only 2% and his check-after fold is following:

At flop 52%
at turn 50%
at river 85%
Flop ($5.25) 2 6 7
CO checks, Hero bets $4.99, CO calls $4.99
Here I see no reason to pot-control, as a risk for check-raise is low.
Turn ($15.23) 2 6 7 5
CO checks, Hero bets $8.00, CO calls $8.00
This was a much closer situation for me, whether I should bet or not.

I still have a gutshot to nuts, but other than that my hand is pretty weak. Against possible calling range I must improve. However, as the risk for check-raise is very low and if it happens, I don't mind folding at all I considered that value is maxed by betting again. Either by getting an immediate fold, hitting lucky nuts at river or being able to bluff again at river. Given the stats of villain I guess that building a pot for river is good strategy when I can usually take the pot down by betting again.
River ($31.23) 2 6 7 5 2
CO checks, Hero bets $18.50, CO folds
Villain has now 15,84$ left. The most tricky spot was here. It is hard for me to think what that villain could actually have to make riverbet profitable. Which hands in his range are still stronger than my pair of sevens but would still fold? Some draws with clubs could still be weaker than my made hand, my pair of sevens have tiny showdown value also.

-7 with better kicker?
-Overpairs?

I don't expect folds from any straights, trips or fullhouses. However the villain had strong stats. Check-after fold at river was 18/20 samples. So despite not being able to tell what could have been the holding for this move, I decided to use stats based approach.

I am still puzzled about the hand with a biggest question. Should I have used the tiny showdown value of my weak pair of sevens instead of making this bluff at river.
Final Pot BN wins $29.67
Rake is $1.56

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