Betting turn or no?

Unknown opponent. I should certainly still be betting turn here to get called by flush and now straight draws, right? Is turn bet sizing fine, and is fold correct? Thanks as always for feedback!

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

BTN: 178 BB (VPIP: 22.22, PFR: 11.11, 3Bet Preflop: 0.00, Hands: 9)
SB: 113 BB (VPIP: 100.00, PFR: 0.00, 3Bet Preflop: 0.00, Hands: 2)
Hero (BB): 129.2 BB
UTG: 84.8 BB (VPIP: 55.56, PFR: 22.22, 3Bet Preflop: 20.00, Hands: 9)
MP: 229.8 BB (VPIP: 31.25, PFR: 29.69, 3Bet Preflop: 5.26, Hands: 65)
CO: 137.6 BB (VPIP: 22.22, PFR: 11.11, 3Bet Preflop: 0.00, Hands: 9)

SB posts SB 0.4 BB, Hero posts BB 1 BB

Pre Flop: (pot: 1.4 BB) Hero has J♠ K♠

fold, fold, fold, fold, SB calls 0.6 BB, Hero raises to 4 BB, SB calls 3 BB

Flop: (8 BB, 2 players) 5♥ 4♦ J♦
SB checks, Hero bets 3.8 BB, SB calls 3.8 BB

Turn: (15.6 BB, 2 players) 2♠
SB checks, Hero bets 11.2 BB, SB raises to 22.4 BB, fold

SB wins 36.4 BB