Should i have bet the river?

Hand converted with online PokerStrategy.com hand converter:

Play hand

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

Known players:
[tg]BU$2.45:///////;SB (Hero)$2.58:///////;BB$2.00:///////;MP2$1.97:///////;MP3$2.31:///////;CO$2.97:///////;[/tg]

Preflop: Hero is SB with J:d, Q:d.
MP2 calls $0.02, 3 folds, Hero raises to $0.08, BB calls $0.06, MP2 calls $0.06.

Flop: ($0.24) J:h, A:d, 2:h (3 players)
Hero bets $0.16, BB calls $0.16, MP2 folds.

Turn: ($0.56) Q:h (2 players)
Hero bets $0.40, BB calls $0.40.

River: ($1.36) 2:c (2 players)
Hero checks, BB checks.

Final Pot: $1.36.
Results follow:

Hero shows two pairs, queens and jacks(J:d Q:d).
BB shows two pairs, aces and twos(6:h A:s).

BB wins with two pairs, aces and twos(6:h A:s).