Did I play my AA correctly? $2/$5 game.

$2/$5 game at Wynn, Vegas.

I pick up AA in the BB.

I 3bet (to $75) an early position raiser’s $25 bet. He’s a young aggressive Euro kid. He called.
Flop As-Kd-8s (2 spades.)
I bet $75 and he called.
Turn As-Kd-8s-3s - bringing the possible flush.
I bet $120 and he pushed for $320 more - How can I fold?
I felt the right move was to call here. I mean, he had called a BIG re-raise pre-flop and now pushed for $320 into a $565 pot.
Even if he has the flush, I can't be drawing dead.
I call, and he shows 6s4s for the flush. River blanks and I lose BIG money.
Played OK?

Calico from St. Louis