I'm on the bubble with the big stack of the table. Should I push with this weak hand?
I would 3 bet 100% of time. On the bubble, in a 3handed spot, with the big stack and Ax hand. You have a high fold equity and a decent hand, push and gain an aggressive image.
+1 I'd push all in.
If the BTN is reasonably aggressive pre, 3betting is fine. He would fold most hands on this spot, and A4o is a fairly strong hand at a 3handed table.