50NL | Boat facing pot donk on bad river

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50NL | Boat facing pot donk on bad river

Blinds: $0.25/$0.50 (6 Players) BB: $37.12
UTG: $24.43
MP: $58.28
CO: $50.00 (Hero)
BN: $78.32
SB: $67.95
Villain is an unknown fun player.
Preflop ($0.75) Hero is CO with J Q
2 folds, Hero raises to $1.50, 2 folds, BB calls $1.00
Flop ($3.25) 3 3 3
BB checks, Hero bets $2.50, BB calls $2.50
I guess this could be debated, since I can't expect an unknown to fold A-hi here. Maybe some trashy K-hi will fold. Mainly worse hands will fold, but that's okay, and I build the pot for the times I hit. Thoughts on the CB?
Turn ($8.25) 3 3 3 J
BB checks, Hero bets $8.00, BB calls $8.00
Nuts. (He can have some quads still, sure). So I bet large enough to set up for a river PSB. I assume he's calling all boats, and potentially some AX (at least AQ, AK if he didn't 3-bet that).
River ($24.25) 3 3 3 J A
BB bets $24.25, Hero folds
Bleh. This could be quads, Ax, or a random spazz with 55 that realizes its hand is no good.

I guess the main concern should be:
- Is this a profitable call?

Thoughts on that?

Second concern:
- I don't want to allow 55 to pot bluff me here profitably.

I basically never have Ax on this river since I wouldn't take this line with it (unless it's AJ perhaps), so the top of my range is KK, QQ. (I guess I wouldn't fold that since I block his AQ, AK, but it's still an unhappy spot). If I fold anything below Ax I will allow random air or pocket pairs to take this line profitably. I don't want to allow that.

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