Well, I would like to point out a few important factors. If your sitting at a table with a punch of pro's, limping UTG with AA is prolly a bad idea, you might as well turn your cards over face up and play the hand.

Especially if you never limp with anything else. If your raising with JJ, QQ, AQ, etc UTG and showing these hands down, if you limp UTG and win a showdown and show AA they will file this into memory forever and ever.

On the hand, if your at your local brick and motar casino with the jokers who can't tell you the last time you won a hand, even if it was the last hand then this play will work alot.

In a tournament, the name of the game is survival. It is important that if you limp up front, and get your raise...dont f around just move in. Espcially if there is a raise and a caller already. You dont want to just min raise or any of that garbage...your giving away your hand to most competant players, and some may call just trying to hit a set.

In your example. If i could put in 400 more after I raised, with 77 to potentially get everything if I hit a 7..then I probably have the implied odds to do so. I am wagering 400 to your whole stack. I won't put in any more money unless I can make a hand that will beat the 2 hands I think you have.
Going broke in the tournament, even with a bad beat, ends your tournament. Its always good to take down that pot pre flop and continue forward.

In a cash game, sometimes a dream scenario occurs where you limp and it folds to a mid position player who raises and then it folds back to you. In this case, you have zero incentive to reriase. Your hand is very disguised and your heads up with AA...great situation.

Most often though, there will be other limpers and perhaps callers, in this case...I prefer to reriase with my AA a large amount to potentially win the pot right there or narrow it down to head up.

It is safer to take chances in a cash game in the way you play your aces, because you can always rebuy if your bad beat and continue playing.