I have no read on villain as he just sat down.
Party Poker No-Limit Hold'em, $ BB (10 handed)

saw flop|saw showdown

MP2 ($130.05)
MP3 ($106.60)
Hero ($98.50)
Button ($32)
SB ($95.96)
BB ($104.05)
UTG ($69)
UTG+1 ($134.74)
UTG+2 ($83.85)
MP1 ($126.75)

Preflop: Hero is CO with , . SB posts a blind of $0.50.
6 folds, Hero raises to $4, 1 fold, SB (poster) raises to $8.5, 1 fold, Hero calls $5.

Flop: ($19) , , (2 players)
SB checks, Hero checks.

Turn: ($19) (2 players)
SB bets $15, Hero raises to $40, SB reraises $71.96 (All-In)

He checked the flop after the reraise preflop. To me this is a sign of hitting a set. My instinct was to fold. How do I play it on the turn?

Stealth

You're probably gone, but you can't fold now. Call and hope he's got AA or AK, thought he clearly doesn't.

You could call down the turn and river in this situation, cause you're not gonna scare off AK or AA (if hes a good player) and not pay so much to the set.

You definitely bet the flop on that one. You don't want to give a free draw. You want to learn where you are in the hand. AK probably calls you too.

I make my stand on the flop which makes your agonizing turn decision less likely.