This hand is an example of a situation in which I believe that we should play AA somewhat passively, given the flop texture and preflop action. I'm pretty comfortable with turn and river action - they seem to play themselves, as villain's range on the flop is a ton of smaller PPs, 7x, and probably an abnormally high number of random floats, with only combos that beat us (of which there are very few) likely to give us any significant action. I'd be interested to hear alternate opinions on this. I'm mainly looking for thoughts on 2 decision points:

1. Preflop 3-bet sizing: given villain's min-raise from UTG, I figured his range to be fairly wide, and decided to size down considerably from standard. My decision was based on a desire to widen both villain's calling and 4-betting ranges here. After the hand was over, I wonder if our stack sizes, being so deep, should have had me sizing up above standard rather than down.

2. Flop action: As I said, I believe this hand should play passively, in general, but I'm wondering if I should have considered checking this flop rather than c-betting. If we are going to c-bet most of the time here, what type of sizing should we be going with? I felt my flop sizing was actually too small, though I'm not inclined to go too much bigger. I'm wondering where we think the best sizing lies, or if we should bet here at all. Protection is clearly not an issue here, so we need to extract max value from a range of hands that is going to have missed a ton.

NL Holdem $0.1(BB)
HJ ($10.41)
CO ($42.95)
BTN ($10.98)
HERO ($54.91)
BB ($11.17)
UTG ($25.92)

Dealt to Hero: As Ah

UTG Raises To $0.20, HJ Folds, CO Folds, BTN Folds, HERO Raises To $0.55, BB Folds, UTG Calls $0.35

Hero SPR on Flop: [21.14 effective]
Flop ($1.20): 7h Js Jc
HERO Bets $0.30 (Rem. Stack: 54.06), UTG Calls $0.30 (Rem. Stack: 25.07)

Turn ($1.80): 7h Js Jc 3c
HERO Checks, UTG Bets $0.85 (Rem. Stack: 24.22), HERO Calls $0.85 (Rem. Stack: 53.21)

River ($3.50): 7h Js Jc 3c 3h
HERO Checks, UTG Bets $1.66 (Rem. Stack: 22.56), HERO Calls $1.66 (Rem. Stack: 51.55)