2/5 Live--AA 400BB deep + theory

[JasonP530]

2/5 Villian liked to gamble and will call anything preflop for a raise, but tends to have a good hand when reraising. Not sure of his standards to call a 4bet. Villian has 2100 and I cover.

1 limper and I raise to 40 with AA. MP cold calls and Villian makes it 340. I am going to reraise it OOP and so deep, but what should I raise to?

Do you reraise anything in this spot other than AA? Is there anything you would call here? I seem to be having lots of trouble in reraised pots where I don't have the lead. Any helpful advice?

Thanks,
Jason