Strong draw in position: river bricks after turn check-behind; villain bets 1/2 pot

Full Tilt - $0.05 NL FAST (6 max) - Holdem - 6 players
Hand converted by PokerTracker 4

Hero (CO): 308.6 BB
BTN: 110.6 BB (VPIP: 26.92, PFR: 19.23, 3Bet Preflop: 0.00, Hands: 28)
SB: 153 BB (VPIP: 22.02, PFR: 7.74, 3Bet Preflop: 1.49, Hands: 172)
BB: 80 BB (VPIP: 35.98, PFR: 7.93, 3Bet Preflop: 1.54, Hands: 166)
UTG: 199 BB (VPIP: 25.83, PFR: 11.56, 3Bet Preflop: 1.32, Hands: 1,206)
MP: 139 BB (VPIP: 27.49, PFR: 7.36, 3Bet Preflop: 3.29, Hands: 474)

SB posts SB 0.4 BB, BB posts BB 1 BB

Pre Flop: (pot: 1.4 BB) Hero has A♣ Q♣

fold, MP calls 1 BB, Hero raises to 4.4 BB, BTN calls 4.4 BB, SB calls 4 BB, fold, MP calls 3.4 BB

Flop: (18.6 BB, 4 players) 9♣ J♦ 5♣
SB checks, MP checks, Hero bets 13.8 BB, fold, SB calls 13.8 BB, fold

Turn: (46.2 BB, 2 players) J♥
SB checks, Hero?