PokerStars No-Limit Hold'em, $0.10 BB (8 handed) Poker-Stars Converter Tool from FlopTurnRiver.com (Format: FlopTurnRiver Cards)

SB ($10)
Hero ($11.20)
UTG ($10.60)
UTG+1 ($11.40)
MP1 ($8.50)
MP2 ($13.20)
CO ($5.65)
Button ($9.40)

Preflop: Hero is BB with , .
5 folds, Button raises to $0.5, 1 fold, Hero raises to $0.9, Button calls $0.40.

Flop: ($1.85) , , (2 players)
Hero bets $0.3, Button raises to $1.3, Hero calls $1.

This was a horrible miss click (i wanted to bet $0.90) and i felt sick until he raised.
Is $0.90 enough here or should i be betting more??


Turn: ($4.45) (2 players)
Hero bets $1.2, Button raises to $4, Hero calls $2.80.

I only bet $1.20 here because i didn't want to scare him off, but now that i think about it i should have bet at least half the pot. Thankfully he raised.

River: ($12.45) (2 players)
Hero checks, Button checks.

How bad is this check?? He can't have the straight (although i've seen stranger things), but if he does, and raises me, can i call??
So i thought if i check he may check it down fearing the straight.

Final Pot: $12.45

He had AK

Did i play this too weak ???? (the miss click aside)