Turn+Second barrel+mano=Push vs Raise?

Hand converted with online PokerStrategy.com hand converter:

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$0.05/$0.1 No-Limit Hold'em (8 handed)

Known players:
[tg]BU$23.23:///////;SB$8.05:///////;BB$4.32:///////;UTG2 (Hero)$4.22:///////;MP1$10.85:///////;MP2$10.15:///////;MP3$9.91:///////;CO$9.85:///////;[/tg]

Preflop: Hero is UTG2 with A:d, J:d.
Hero raises to $0.40, MP1 folds, MP2 calls $0.40, 5 folds, 4 folds, 3 folds, 2 folds, BB folds.

Flop: ($0.95) 9:h, 3:s, J:s (2 players)
Hero bets $0.70, MP2 calls $0.70.

Turn: ($2.35) K:s (2 players)
Hero bets $1.15, MP2 raises to $2.96, Hero raises to $3.12, MP2 calls $0.16.

River: ($8.59) T:s (2 players)

Final Pot: $8.59.

Hola a todos:
No sé si es mejor hacer bet/fold en el turn en esta situación.
Agradezco sus comentarios.