River Raise Bet Sizing Facing Min-Bet

[StageWhisper]

I wouldn't imagine this coming up that much in higher stakes games, but I run into this often enough in $10NL to ask:
How do you size a value bet in position when villain min bets on the river? Do you bet in relation to the pot or the bet? Has anyone come across this line and been re-raised?

Example:

Full Tilt Poker
No Limit Holdem Ring game
Blinds: $0.05/$0.10
5 players
Converter

Stack sizes:
UTG: $12.30
CO: $8.30
Hero: $9.65
SB: $4.95
BB: $2.70

Pre-flop: (5 players) Hero is Button with A K
UTG folds, CO raises to $0.2,Hero raises to $0.75, 2 folds, CO calls.

Flop: 5 J K ($1.65, 2 players)
CO checks, Hero bets $1.65, CO calls.

Turn: 9 ($4.95, 2 players)
CO checks, Hero bets $2, CO calls.

River: A ($8.95, 2 players)
CO bets $0.1, Hero ???

Check my line here, too...bet more on the turn?

[Renton]

i'd make it 1.0 preflop (to get more money in and make postflop easier)

then i'd bet like 1.8 into 2.2 on the flop, then i'd commit on the turn.

As played just raise whatever u think he will call. Probably to something like 3.50

[StageWhisper]

Bet sizing is definitely something I need to work on. I think playing on Full Tilt has kept my bets lower than they should be. The average $10NL pot on the 6max tables is $1.50.

I bet $3 on this river. I'm not sure villain would even call $1.

[larsmars]

Has anyone come across this line and been re-raised?

Monster line from an inexperienced player.

[XTR1000]

i see this line quite often at 25nl. most of the time it´s a busted draw. in this spot i like raising to ~ 2/3 to 3/4 pot, which might get a call from weaker K/2pair.

[Ash256]

QT scares me, but this needs raising. Would a push only get better hands to call?