Villain had been a little weak, calling with a lot of hands, opening a few, but rarely continuing unless they had hit the flop in some fashion.

PokerStars No-Limit Hold'em, $0.02 BB (9 handed) - Poker-Stars Converter Tool from FlopTurnRiver.com

Button ($1.42)
SB ($3.08)
BB ($2.96)
UTG ($1.10)
UTG+1 ($5.75)
Hero (MP1) ($1.89)
MP2 ($0.84)
MP3 ($2.94)
CO ($4.58)

Preflop: Hero is MP1 with A, 10
UTG calls $0.02, UTG+1 raises to $0.10, Hero calls $0.10, 7 folds

Flop: ($0.25) Q, 4, J (2 players)
UTG+1 checks, Hero bets $0.20, UTG+1 calls $0.20

Turn: ($0.65) 9 (2 players)
UTG+1 checks, Hero ?

Arguments for and against betting?

Since I picked up a nine on the turn, I was looking at a double gutshot and a nut flush draw. 9 flush outs+4 untainted straight draw outs.

Villain's range:
77+, A10+, QJ+

He didn't seem like a slowplayer, so it was unlikely he was check-calling a set or an overpair. He overbet a few hands earlier in the session and had gotten some dumb callers.