BB connundrums in the 100K

[AragornX151]

Hi all,

Been taking some time away from online poker for awhile to focus on other things and to study/think about my game, but decided to play the 100K last night on Stars. A situation came up that I'm still unclear on the optimal line for.

Stacks: UTG 4.4K
Me: 12K~
Blinds: 200-400 + 20 ante

My image should be tight-aggressive, as my two resteals were not called. That said, UTG seems fairly weak, though not a complete moron, and had mini-raised several times before (albeit when the stacks were deeper). His PokerDB is essentially nonexistent.

About 200 people remain, 120 pay, which obv. doesn't matter to me but may to a lower-stakes player/sat. qualifier?

UTG mini-raises to $800, leaving him with $3600 behind. Everyone folds to me in the BB with AdTd. What's your play, and how do you proceed with the hand? Every line seemed severely flawed to me, and wrought with problems; ATs might be the most annoying hand to hold here.