AA in SB against insanely tight BN

[xtwalker]

Friday night I was playing on a bad, uber tight 3/5 NL table for a few hours (on the list to move to another table.) I had decent-good reads on most of the table and I have thousands of hands with the BN and knew his raising standards pretty well. (mostly know his play from tournies, limit games, and a few NL tables) I also knew he was starting to tilt from being a little cold decked.

It was folded around to the CO ($300) who raised to $20. He didn't seem very strong and I thought he was making a play at the blinds.

The BN ($400) raised to $60 and I knew he had JJ or better, and did not have AQ or AK bc he always plays those hands too softly and under-values them. The key to me, is I know he has JJ+ here 99.9% of the time. I have never once seen him 3-bet with less.

I had AA in the SB, and about $500.

How much should I re-raise here? Should I consider a smooth call and play him out of possition? I know that all of us being < 100bb makes a difference, how much should I let it affect this play?