$10 NLHE 6-max: Bet sizing input requested

Im trying to get a better grasp on bet sizing.

Should I have folded this river?

full tilt poker $0.05/$0.10 No Limit Hold'em - 6 players - View hand 909496
The Official DeucesCracked.com Hand History Converter
UTG: $10.54
MP: $8.10
CO: $3.91
Hero (BTN): $13.42
SB: $12.92
BB: $4.94
Pre Flop: ($0.15) Hero is BTN with Q :spade: J :spade:
3 folds, Hero raises to $0.30, 1 fold, BB calls $0.20
Flop: ($0.65) T :diamond: 9 :spade: Q :club: (2 players)
BB checks, Hero bets $0.40, BB calls $0.40
Turn: ($1.45) K :diamond: (2 players)
BB checks, Hero bets $0.66, BB calls $0.66
River: ($2.77) 2 :diamond: (2 players)
BB bets $3.58 all in, Hero calls $3.58
Final Pot: $9.93
Hero mucks Q :spade: J :spade:
BB shows A :diamond: 9 :diamond: (a flush, Ace high)
BB wins $9.27
(Rake: $0.66)

I don't understand why your opponent would go all in on the river with the nut hand. I wouldn't think he had it if he pushed on the river like that. That's the only reason he did it as far as I can see.

I like a pot-sized bet on the turn here. Only AJ beats you at that point, he can't fold his 2-pr or trips, and he should fold hands like the one that ended up beating you.

I think the turn bet should have been 3/4 pot.

Like $1.08 or something.

I'd bet more on the flop and turn. fold the river as played.

Turn should be more, something north of $1.

How bad was your opponent here???

Against anyone remotely competent the river is a fold. You're calling with about the 15th best hand hoping for a split. Generally not a good idea.