I find myself I'm in this spot semi-regularly and I'm wondering how you feel the best way to play it is.

Live 1/2:

We have a big hand UTG. Let's say it's AA for right now (but I would like thoughts on 88-TT, JJ-KK, AK)

We raise to $15, get 3 callers by players playing between $75-300, and then a short stack shoves for $30, opening the action back up again.

I understand that the stack sizes of the callers matter when deciding what to do here, but in general, is it more profitable to

--re-raise big here because we'd be OOP for the hand in a bloated pot, (virtually guaranteeing everybody else folds, and we get heads up as a favorite with good overlay, but potentially miss some value from bigger stacks)

--re-raise small here to induce calls, and create a side pot that could create an illusion we're bluff c-betting or something?

--call to keep weaker ranges in the pot?

How does our actual hand (as opposed to our EP range) play into this decision, i.e. are you making different moves with different hands? I find myself in general just raising big in this spot to take the guaranteed profitable spot, but I'm almost annoyed when this happens and feel like I'm sometimes missing value.

Depends a lot on factors that you pointed out matter.

In general, I'd be ok to play AA/KK/AKs multiway. We're so far ahead of everyone's ranges that I will take the variance of losing.

More vulnerable hands I'm looking to put raises in with. Hands like 99, 88 I might reraise big. AKo/QQ/JJ would probably be smaller. TT in between.

AA I might raise to $65 and see if I can keep one caller in. Most other hands I'll raise to $100+ and just take the heads up. Even KK can be hard to play out of position because an ace flops one in four times and you are stuck check/deciding.

+1

Just calling here when it gets back to you would be just about as bad as being in the BB with AA and just calling after someone else raised to $15 and got 3-4 callers. Reraising is a must. If anyone is going to outflop you, they need to do it after putting more money in than they already have.

Almost never with AA or KK. TT-AK I wouldn't make it huge but the pot is already pretty big at $90. If you are 100 BB deep and raise to $75(pot sized bet) that should make any and all flop decisions easy as you have a SPR of 1.
With AA and KK, I would raise to maybe $60. If you get 1 caller, the pot will be $180 and with a starting stack of 100 bb, you and villain should have $140 behind. This seems easy.

Never with TT or better. Your call will cause a cascade of calls. Even with AA, this would be too much FPS.