Nut Flush Draw OTF - Line Check

I've had a couplefew spots like this recently, and they always feel spewy at the time when they don't pay off. Thoughts/Comments?

$0.05/$0.10 No Limit Holdem
PokerStars
5 Players
Hand Conversion Powered by weaktight.com

Stacks:
DoubleJ (UTG) ($11.25) 113bb
CO ($11.32) 113bb
BTN ($11.15) 112bb
SB ($8.92) 89bb - VPIP:50, PFR:33, 3B:0, AF:12.0, FoldTocBet:1 out of 2, Hands:42
BB ($10.25) 103bb

Pre-Flop: ($0.15, 5 players) DoubleJ is UTG

I've seen SB call raises from the blinds w/ K6o and J2s, so i'm raising here to ISO

DoubleJ raises to $0.35, 2 folds, SB calls $0.30, 1 fold

Flop: ($0.80, 2 players)
SB checks, DoubleJ bets $0.50, SB raises to $1, DoubleJ calls $0.50

I'm raising here to either take it now, or build the pot (?). He CIB's which is neither unexpected nor unwelcome.

Not sure I can put him on much of a range here (?); prolly some TPs, mebbe Straights/Sets/2Ps/Draws. w/e, he seems to like his hand, so i reckon I'll get paid off if I hit. I call w/ 4.6:1

Turn: ($2.80, 2 players)
SB bets $1, DoubleJ calls $1

He leads Turn and i call w/ 3.8:1 explicit, which is a bit short, but as above i'm pretty conf i can get at least another bet if I hit. (Also not sure what to make of his sizing here....)

River: ($4.80, 2 players)
SB bets $3, DoubleJ ???

Our Studio Audience said....Uh Ugh

hero folds river i suppose. all prior street are played well. nh