Rivering straight; villain checks river after he had raised turn

PokerStars - $0.02 NL (6 max) - Holdem - 5 players
Hand converted by PokerTracker 4

Hero (BTN): 252.5 BB
SB: 100 BB (VPIP: 19.63, PFR: 13.58, 3Bet Preflop: 1.79, Hands: 166)
BB: 100 BB (VPIP: 16.18, PFR: 10.29, 3Bet Preflop: 4.55, Hands: 72)
UTG: 100 BB (VPIP: 46.15, PFR: 38.46, 3Bet Preflop: 33.33, Hands: 13)
CO: 134.5 BB (VPIP: 23.08, PFR: 19.23, 3Bet Preflop: 0.00, Hands: 28)

SB posts SB 0.5 BB, BB posts BB 1 BB

Pre Flop: (pot: 1.5 BB) Hero has 6♠ 6♦

fold, fold, Hero raises to 3 BB, SB calls 2.5 BB, fold

Flop: (7 BB, 2 players) 4♣ 5♦ 9♥
SB checks, Hero bets 4.5 BB, SB calls 4.5 BB

Turn: (16 BB, 2 players) 3♥
SB checks, Hero bets 8 BB, SB raises to 24 BB, Hero calls 16 BB

River: (64 BB, 2 players) 2♣
SB checks,

His river check looks a lot like he was either semibluffing a flush draw OTT or he is afraid of a straight now with 2pair or set.

So what should my river size be?