Phoenix Wright
Legend
Loyaler
Stack sizes, effective stacks and position at the table are all critical details left out. Generally speaking, you want to be open raising (like 3bbs you mentioned) for value with AA. If you are shorter stacked (roughly 20bbs or less), then you need to determine how you want to proceed to probably get as many chips in as possible. It might be just one shove All-in, or it might be a combination of bets to get All-in by showdown.
The only "exception" to go All-in when deeper than this is if you really think the opponent is going to get out of line and call with a worse hand. The problem is that if you shove All-in with more than 20 bbs, a reasonable opponent will usually fold and all we get are the blinds and antes (which still isn't too bad though) whereas raising and calling versus just going All-in right away gets a few more chips than them folding to a shove.
The only "exception" to go All-in when deeper than this is if you really think the opponent is going to get out of line and call with a worse hand. The problem is that if you shove All-in with more than 20 bbs, a reasonable opponent will usually fold and all we get are the blinds and antes (which still isn't too bad though) whereas raising and calling versus just going All-in right away gets a few more chips than them folding to a shove.