100bb effective stacks

1) UTG Raises, all folds to hero who has AA. Hero 3bets to 3x the UTG's raise right?

2) UTG Raises, all folds to CO who overcalls, hero still has AA. Hero 3bets to 3x the raise +1 for the overcall, right? So it's 4x the raise here?

3) UTG Raises, everyone calls to hero on the button who still has the AA, Hero 3-bets to 3x the raise +6 for the overcall meaning he's raising to 9x the original raise?

This doesn't seem right.

Most importantly what's the "math" behind the 3-bet as to WHY a certain size of raise seems standard.