[Closed] [MSS-NL5] hero has 2nd pair, villain bets small on river

In general the situation is:
1) hero has top pair (or overpair) at flop, value bets and one opponent calls
2) turn brings a higher card (usually A or K) and both check, now hero has 2nd pair
3) river is irrelevant and villain bets really small (20-30% of pot)

Here is an example.

Hand converted with online PokerStrategy.com hand converter:

Play hand

$0.02/$0.05 No-Limit Hold'em (9 handed)

Known players:
[tg]BU (Hero)$2.01:///////;UTG1$12.50:///////;[/tg]

Preflop: Hero is BU with J:c, J:d.
UTG1 calls $0.05, 4 folds, CO raises to $0.10, Hero raises to $0.35, 2 folds, UTG1 calls $0.30, CO folds.

Flop: ($0.87) 5:c, 9:h, 3:h (2 players)
UTG1 checks, Hero bets $0.65, UTG1 calls $0.65.

Turn: ($2.17) A:h (2 players)
UTG1 checks, Hero checks.

River: ($2.17) 6:s (2 players)
UTG1 bets $0.45, Hero calls $0.45.

Final Pot: $3.07.
Results follow:

UTG1 shows a pair of aces(A:c 4:c).
Hero shows a pair of jacks(J:c J:d).

UTG1 wins with a pair of aces(A:c 4:c).

Here villain bets 20% of pot here on the river. This means that I need to win at least 1 of 7 times to have profit, right?
How whould you play the river?
Would it be better to bet small on the turn?