Playing AA post flop depends on a variety of factors.
Numbers of villains in pot.
These are just some dynamics off the top of my head.
On Kc10s3d board for example...
First, consider hands that will call your bets... K-x, Q-J, PPs maybe like QQ and JJ, some 10x hands too (like A-10s with back door flushes perhaps).
Next, consider hands that may raise your bets (villain dependant). 2p, sets, TPTK, maybe OESD might raise you if they think you have air.
So if you can nail a range down, get value from worse hands and draws (don't pay off draws if they do hit if possible). Fold to better hands. Simple (not really, but it can be with good hand reading).
I don't think it's a good idea to try and shove to fold draws out. You are missing value. Bet enough that the price is bad for them to draw, but not enough to fold them out. That is the sweet spot. If they call a full pot bet with a naked FD, they are kinda making a mistake, and you will win from villains doing this in the long run.
So if you think villain has a hand you are beating, bet.
Bet on the K-10-3 board on the flop.
Raises in general mean more serious hands as the hand progresses. River raises are usually from pretty strong hands. Flop raises can be many hands that you might be ahead of.
I am just kinda rambling here. Sorry for that. I am just trying to list my thoughts on the issue.
So if all you have on the river is one pair (AA), and villain is making a big raise, you are probably behind (once again villain dependant).
Just play the rockets with caution, don't get wrapped up with them and forget to think about what the opponent has considering the board.
As for your image on the table....
If you have recently showed down some rags, or got caught in a bluff, etc, people might play back at you more.....
If every time you showdown you have monsters, people may play more cautiously vs you.
But remember, when you consider how you are perceived to others, think about the info they have to base their image of you on. Remember what hands opponents have seen, not the hands that did not make it to showdown.
For example, if you raised 9-2s on the button, and flopped a monster and stacked someone, people will remember that. They may think of you as the dude who raises with rags and plays bingo, just because if that one hand....
So they may flop TP crap kicker on K-10-3 board, and think they have you crushed, if you have gotten out of line recently.
These are just some random thoughts to consider when deciding how to play post flop with a hand like AA. Hope it helps.
Just remember, I this one pair. If villains are blasting away 3 streets, they most likely have you beat (depends though).