10NL: Overpair facing turn shove

[alexDJI]

Poker Stars - No Limit Hold'em Cash Game - $0.05/$0.10 Blinds - 6 Players - (LegoPoker Hand History Converter)

SB: $4.50
BB: $7.90
UTG: $9.85
MP: $4.70
Hero (CO): $27.85
BTN: $10.25

Preflop: Hero is dealt (6 Players)
UTG folds, MP calls $0.10, <font color="red">Hero raises to $0.50</font>, BTN calls $0.50, 2 folds, MP calls $0.40

Flop: ($1.65) (3 Players)
MP checks, <font color="red">Hero bets $1.60</font>, BTN folds, MP calls $1.60

Turn: ($4.85) (2 Players)
<font color="red">MP bets all-in for $2.60</font>, Hero ???

Villain hasnt played a hand that went to show down and played pretty tight. He seemed passive though.
It looks like a draw that hit, or an overpair, or a combo draw to me. I really like my hand and think I have to call, but I'm not really sure.
Comments on PF and flop are welcome.