I recommend using the same decision process for deciding whether to three-bet Aces as you would any other hand. From my experience, many players have a distorted bias towards Aces. They view them in a completely different perspective than all the other hands. Several months ago I was going over a hand with a student where he decided to three-bet very raggedy aces in a button vs cut-off situation. I asked him why he decided to three-bet, and he simply replied, “Because I have Aces.” I asked what he would’ve done with raggedy Kings, and he said he would’ve just flat-called. I found this amusing, because given the stack sizes and table dynamics, raggedy Kings and Aces play very similarly in a spot like that. What I eventually got him to realize is how important it is to view a starting hand in terms of the post-flop scenario it creates for The Big Three.
Anyhow, stack sizes greatly affect the decision of whether to three-bet Aces or not. With weaker Aces, try to commit approximately 40% of your stack pre-flop so you can shove any flop. If you three-bet for 10% or 20% of your stack, it becomes awkward on many flops, because with weak Aces, you’ll be left with a dry overpair on 80% of boards. This rule doesn’t apply for the premium Aces hands, simply because they have such good coverage on a wide variety of flops, so they’re comfortable in three-bet pots at any stack depth regardless of the number of players.