A weird PF situation with JJ

[DavidC]

5-5 NLHE, 500 buy in. Villains have 2k+ and hero has 500.
Villain on the button is a loose aggressive guy who is on a super-heater. Villain in the BB is a guy who knows me as a tight, solid player. I think he thinks I'm a little weak post-flop, but I'm not sure. There are about 8 players at the table.

PF: 2 callers and villain raises on the button to $50. In the SB I reraise to $200 (villain's made raises like this with hands like ATs, JTs, JTo, etc.). The BB calls.

The players that limped are generally guys that will limp with garbage and fold to a reraise.

The BB is very loose in SH LHE, and pretty tough in HU NLHE, but has been playing this game very very tight... I'm guessing that he's under-rolled for it.

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What do I put the BB on?

FWIW, I think AA/KK is appropriate, maybe AK, but I think he mucks QQ and AQ. So I guess my main question is, would he have AK?

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Edit: Also, if I were to just call, it's quite possible that the limpers would call along unless BB were to reraise.