Full Tilt Poker $0.05/$0.10 No Limit Hold'em - 5 players
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2+2 Hand Converter
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Hero (SB): $13.53
BB: $16.62
UTG: $3.20
CO: $10.15
BTN: $3.73
Pre Flop: ($0.15) Hero is SB with A

A

UTG calls $0.10,
1 fold, BTN calls $0.10,
Hero raises to $0.50,
BB raises to $1.80,
2 folds, Hero calls $1.30
Flop: ($3.80) 7

J

7
(2 players)
Hero checks,
BB bets $2, Hero calls $2
Turn: ($7.80) K
(2 players)
Hero checks, BB checks
River: ($7.80) 6
(2 players)
Hero bets $7.80, BB calls $7.80
Early in a session, no real read on the opponent.
Wondering about several things here.
First, the call of the BB's 3bet when I'm oop with AA preflop instead of making a 4bet or shove. I called because I figured the opponent would cbet the flop. I figured the risk of a bad flop for aces was outweighed by the chances of making more money by just calling preflop and then playing appropriately to maximize the amount of money I might win with aces. A mistake in general at the micros? What would you have done?
Second, how the rest of the hand played out, especially the pot size river (value?) bet after the action went check/check after the flush got there on the turn. Would a smaller value bet have been better...or look too much like I wanted a call with a much stronger hand than I had?
How could my play in this hand have been better and why? How would your advice change at the different micro stakes?
Thanks!