Honestly, I do not think this is a good play. BB was defending his BB from the Hero on the button. 963 is well within his range there. Since BB did not 3-bet pre-flop, you can put him on a drawing hand like 56s to 89 or J10. My preferred action here would've been to check the flop instead of placing the continuation bet since it was a garbage flop and likely hit your opponent more than you.
If your starting hand was JJ - AA or even 78 or 910, I think your play would have been a good one.
RE: Is this play is good (middle stack, flop all in play)?