Villain new to table.

PokerStars No-Limit Hold'em, $0.50 BB (4 handed) Hand History Converter Tool from FlopTurnRiver.com (Format: FlopTurnRiver)

Hero ($93.20)
Button ($28.75)
SB ($47.30)
BB ($55.05)

Preflop: Hero is UTG with 7, 6.
Hero calls $0.50, Button calls $0.50, 1 fold, BB checks.

Flop: ($1.75) 8, Q, 5 (3 players)
BB bets $1.5, Hero raises to $4, Button folds, BB calls $2.50.

Turn: ($9.75) 6 (2 players)
BB checks, Hero bets $5, BB raises to $16, Hero ??

smells like a set, which means my flush has one less out. He's definitely calling a push. If he does have a set, we're a 2-1 dog.

Do you think I should have checked Turn in hopes to see river cheaply? Villain liked his hand enough on flop to lead a call a re-raise, so perhaps I should have proceeded with more caution after a turn blank (i.e., we likely have no fold equity for this bet, so are we just raising a pot for no reason after whiffing?

It seems a Check-Call would have been the best option on turn.

Does anyone here call?