[25NLz] 3b, thin value, too thin?

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[25NLz] 3b, thin value, too thin?

Blinds: $0.10/$0.25 (6 Players) BN: $57.47 (Hero)
SB: $9.40
BB: $39.97
UTG: $33.01
MP: $28.01
CO: $25.60
Preflop ($0.35) Hero is BN with Q Q
2 folds, CO raises to $0.67, Hero raises to $2.12, 2 folds, CO calls $1.45
Villain is 16/12 over 250 hand sample and folded to 3/5 3bets. I can sometimes 3b as low as 55+ BN v CO, but against his tighter open it is more like 77+ for pairs. I have most suited broadways and AJ+ KQ, some lower suited aces and occasional suited connectors.
Flop ($4.59) 3 7 6
CO checks, Hero bets $2.28, CO calls $2.28
Should I have a betting range at all here? There are lots of turns that I want to protect against which is why I chose to bet. I can have 77 and maybe 66, but he can plausibly have all the sets. I don't think he ever has 45. I have occasional 98 and T9 that would like to bet.
Turn ($9.15) 3 7 6 K
CO checks, Hero checks
River ($9.15) 3 7 6 K 4
CO checks, Hero bets $4.54, CO calls $4.54
Is this too thin? I want value from 88-JJ, but now 44 and 55 have improved, and maybe he has some frequency AK, so this might be a bad idea. I am hoping he bets enough with 55 and his sets to not value cut myself. I have plenty of air that could want to stab, but I am not sure which air I would actually bluff with here. I can also have non-spade A5s so he doesn't fold my entire range by raising.
Final Pot BN wins and shows a pair of Queens.
BN wins $17.41
Rake is $0.82

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