re: Poker & How to place BB on a hand?
A-10 on a multi-way pot in position is auto-reraise for me. Yes, it's not the "best" hand, but you may push out one or two with a standard 3x to 4x bet.
As for your hand referenced, without suits, I couldn't tell you if the BB was on a straight draw with 3-5, 5-6, or 8-9, or if there was a flush draw in the works. Based upon limp, 1/2 pot, check-push, I would say he's got 8-9 going for the OESD and trying to bully you off the pot. Alternatively, he could have pocket Jacks and trying to buy the pot so you don't hit something bigger on the river.
More info needed. Is this a freeroll (I'm insta-calling here) or a real-money tournament?