Call this unknown's push with JJ?

[Logik]

PokerStars No-Limit Hold'em, $0.50 BB (6 handed) FTR converter on zerodivide.cx

UTG ($81.35)
MP ($53.90)
CO ($29)
Button ($42.95)
<font color="#C00000">Hero ($81.10)</font>
<font color="#C00000">BB ($10)</font>

Preflop: Hero is SB with J[img]/images/graemlins/club.gif[/img], J[img]/images/graemlins/spade.gif[/img].
<font color="#666666">4 folds</font>, <font color="#CC3333">Hero raises to $2</font>, <font color="#CC3333">BB raises to $10</font>...

Literally the BB's first hand. He waited to post his blinds, and this hand was it. He may have noticed that I have been stealing with position.

I raise to only $2.00 because it drives out weak hands, and I've been raising to $2.00 almost every time I was in the SB and its folded to me. He re-raises all in.

What this tells me:
1) AA doesn't re-raise all in, because he still has a lot of fold equity with a push.
2) KK doesn't re-raise all in, for reasons in #1
3) QQ might do this.
4) AK might do this.
5) Any other hand might do this.

The only hand that I'm worried about then its the other JJ or QQ.

What's the play?