PokerStars No-Limit Hold'em, $0.05 BB (7 handed) - Poker-Stars Converter Tool from FlopTurnRiver.com

Hero (CO) ($5.10)
Button ($12.55)
SB ($5.08)
BB ($3.82)
UTG ($5)
MP1 ($9.20)
MP2 ($4.86)

Preflop: Hero is CO with ,
3 folds, Hero bets $0.20, 1 fold, SB calls $0.18, BB calls $0.15

Flop: ($0.60) , , (3 players)
SB checks, BB checks, Hero checks

Turn: ($0.60) (3 players)
SB checks, BB bets $0.30, Hero raises to $0.90, 1 fold, BB calls $0.60

River: ($2.40) (2 players)
BB bets $1.50, Hero?

Not a whole lot to go on. SB and BB have been in 30% of hands, but I have only 20 hands on each.

Flop, I elect not to c-bet here.
Turn, I'm thinking a raise to $1.10 seems a little better as it sets up for ~pot sized bet on river to put him all in. I'm having a hard time ranging this hand outside Qs9s, QsTs, QsJs, maybe KdJd and 2pr type hands and sets, however I'm leaning more towards drawing hands with a piece of the board cause he calls my raise and doesn't re-raise. I suppose there could be Ax in his range, but I would expect him to bet the flop.
River, In all honesty, this looks like a value bet. Now there is no way I am folding here. What I am trying to figure out is if I should shove over, he has like $1.20 left behind.