$10 NLHE 6-max: Did I play this optimally?

Villian Stats (VPIP/PFR/AF): 16/9/2.3

I'm partly doubting my play here and partly thinking I played it right. The main thing I'm obviously thinking is that this player has Ax and has hit a straight on the turn making me check it OOP. Is that the right move or should I have continued to bet knowing that he may have caught a flush draw and carried on for the ride?

IPoker Network $10.00 No Limit Hold'em - 6 players - View hand 2129669
DeucesCracked Poker Videos Hand History Converter

SB: $7.14 - VPIP: 57, PFR: 11, 3B: 43, AF: 1.3, hands: 37
BB: $10.00 - VPIP: 15, PFR: 15, 3B: 7, AF: 4.5, Hands: 174
UTG: $13.39 - VPIP: 19, PFR: 16, 3B: 13, AF: 8.0, Hands: 63
Hero (MP): $10.74 - VPIP: 18, PFR: 14, 3B: 4, AF: 2.4, Hands: 62829
CO: $10.00 - VPIP: 16, PFR: 9, 3B: 8, AF: 2.3, Hands: 43
BTN: $14.51 - VPIP: 57, PFR: 11, 3B: 43, AF: 1.3, Hands: 37

Pre Flop: ($0.15) Hero is MP with J J
1 fold, Hero raises to $0.30, CO calls $0.30, 3 folds

Flop: ($0.75) J Q T (2 players)
Hero bets $0.60, CO calls $0.60

Turn: ($1.95) K (2 players)
Hero ??

Hoping he has a flush draw? Doubt he's ever calling with any QsXs combinations here Q9s is a distant possibility. If he had the As he already has the nuts on turn.

Check call up to an 80 percent pot size bet if you ask me. Then shove the turn when board pairs.

If not...check/fold

Can someone. More experienced comment though? Seriously xd

check/call and bet paired board on turn but it kinda turns your hand face up.

but it depends, what's his fold to cbet. because if it's small I would barrel because that means he floats a lot to bluff on turn or river.

Also if you bet, and he doesn't raise, and board gets paired your full boat will be much better disguised.

Wow. To be honest from that board I would fold. He probably has ace 10 and you are right that he probably hit that straight. Sometimes you just have to fold or at least check/fold.