Stabbing at pots

[Spicymoose]

Button open limps, you complete in the SB, and BB checks.

Flop is AJ2r.

Button is obviously bad, and is pretty passive overall. BB is a bit unknown, but is a bit too loose, and can be too agressive sometimes.

What hands do you bet here?

A3? 44? KT?

Do you ever try to check raise?

Are there a lot of hands that you check fold, only because you would rather have better reads on your opponents?