[NL2] JJ set on a dangerous board?

Hand converted with online PokerStrategy.com hand converter:

Play hand

$0.01/$0.02 No-Limit Hold'em (6 handed)

Known players:
[tg]BU$1.88:///////;SB$1.99:///////;BB$2.11:///////;MP2$2.00:///////;MP3$2.77:///////;CO (Hero)$2.19:///////;[/tg]
No notes. The villain is short though, so presumably fish.

Preflop: Hero is CO with J:d, J:c.
2 folds, Hero raises to $0.06, BU calls $0.06, 2 folds, BB folds.

Flop: ($0.15) Q:d, A:c, T:s (2 players)
Hero bets $0.09, BU calls $0.09.

Turn: ($0.33) J:h (2 players)
Hero bets $0.21, BU calls $0.21.

Now this. We hit a set, but I'm not sure if we like it or not. I bet hoping that 2P will still pay, and there's no way I'm check/folding a set, there shouldn't be that many kings there.

River: ($0.75) 5:s (2 players)
Hero checks, BU bets $1.52, Hero folds, BU gets uncalled bet back.

I decided to play pot control and check, planning to call a small bet, like 1/2 pot size. This is a big bet though, so I assumed the villain somehow had a king there and folded.

Anything wrong here? Thank you!

German