I think you actually played the hand pretty well! We want to have some strong checks on those kind of flops after we 3bet pre for balance, and I think AA with the ace of hearts is literally the PERFECT hand to do it with.
Preflop: Standard squeezing spot after an open and a call, can get a lot of value from worse
hands. Even though we have aces, I would have prefered to see a larger raise size from OOP, probably to something like $.70-.75 cents. When we 3bet
bluff in this scenario, we want to maximize our fold
equity and raising to 3x the open, plus an open size raise for every call and plus another 2 big blinds for being OOP, I think that's the best size for our entire range.
Flop: I really like the check here! We definetly are going to be checking quite a few hands on this flop that complete wiff, like AK, AQ and bet some overpairs like 10s, JJs, QQs and maybe KK without a heart. But as I mentioned earlier, I think checking AA with the ace of hearts is an outstanding hand to check here for deception and to protect our range.
Turn: I think continuing our check/call line here is fine, I think a leadout here would be weird especially if we get raised. So as played on the flop, I like the decision to check with the intention of calling here, which is what you were going to do!
River: I think a value bet is mandatory here, as there are a lot of second best hands we can get value from and I would imagine all of villains flushes, two pairs and sets would bet turn the vast majority of the time. However, when we get jammed on, I don't think that villain is ever jamming worse hands here. Nothing really makes sense for him to be
bluffing with that would check the turn, and there are a ton of better hands villain can definetly have on this board runnout. It sucks to fold AA when you've really underrepped your hand, but I just don't see a lot of 5NL players bluffing in this spot. A jam on the river in the micros is almost never a bluff, it's 99% value unless you're playing against an insane person. However, besides the call on the river, I think you played the hand great!