Should I fold a flopped set on the river?

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Should I fold a flopped set on the river?

BN: $5.99
SB: $10 (Hero)
BB: $14.95
UTG: $14.75
HJ: $10.35
CO: $9.47
I've got 75 hands on the villain, he's 25/22. AF of 6.5, which is 14, 8 and 1 on the flop, turn and river respectively. Winning player, seems reasonably decent.
Preflop ($0.15) (6 Players)
Hero was dealt J J
UTG raises to $0.30, HJ folds, CO folds, BN folds, Hero calls $0.25, BB folds
Villain si going to be opening suited broadways, AJo+ and mot, if not all, PPs. I elect to call in the SB. I didn't feel I had that much value against his UTG range and don't want to turn it into a bluff, or play a bloated pot OOP, but would welcome thoughts on 3 betting this?
Flop ($0.70) J 8 2 (2 Players)
Hero checks, UTG bets $0.52, Hero calls $0.52
Near enough dream flop for me, with top set. Villain is agro, cbetting 100%, so I check and he duly obliges. Given his high cbetting, I can't really narrow his range down, I would certainly cbet nearly all my range on a board like this. I elected not to raise, not wanting to fold out his weaker hands and giving him the chance to fire again, the only likely hands which could really call a raise are 22, 88, QQ+.
Turn ($1.74) K (2 Players)
Hero checks, UTG bets $0.87, Hero calls $0.87
Ghastly card for me completing the flush. On the plus side, villain picks up a lot of equity with his broadways making two pair, gutshots and so on. I think he would again barrel most of his range here.
River ($3.48) A (2 Players)
Hero checks, UTG bets $2
Another overcard to my set and completes a probably unlikely q10 straight draw. Villain's AF has been low on the river but he makes a decent be

I get the distinct impression here I could be second best. Problem is I haven't really been able to narrow down villain's range because I've played so passively and he's very aggressive. He would certainly take this line with KK+ and his suited broadways which make a flush.

My guess is his range is 22, 88, QQ+, AJo+, KQo, QTs+, KTs+. I could maybe discount KQo, QQ hands, which he may just check behind for showdown value rather than turn in to a bluff.

Thoughts as to how I played it? Should i be raising the flop or another time?

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