Ace-Nine offsuit 3 handed

Party $33. First hand of 3 handed

Hero 1120t
SB 720t after posting 200t
BB 5560t after posting 400t

Hero dealt Ace-Nine offsuit and pushed. BB had not been raising much or calling with any 2 card when we were 4 handed and he was getting decent pot odds. SB had Pushed majority of past 5 hands or so. Should I have let him push to see if he got knocked out to move up to second? I was thinking I would most likely steal and be able to call his push next hand and still be in decent shape if I lost that one. BB ended up calling (semi bad beat) but I was mainly wondering how many people push here why/why not.