How to fix a stripped hole in a plaster wall?
Screws in wallboard do not support anything. Unless your screws hit a stud or an anchor of some sort, the bracket is decorative, not functional.

If there is not a stud in the immediate vicinity, you need to use a serious anchor. I would recommend using a strap toggle type anchor behind the bottom screw and one of the top screws. 



The bolt can be replaced with a flat head version if you need that for your bracket.

I would use a plastic anchor for the third hole.