First, loosen the arm until it is moving freely. Next, open the throttle to full capacity while making a note of which direction the arm moves in when the throttle moves through it. Once the throttle is fully opened, move the governor shaft in the same direction the governor arm traveled.
https://www.hunker.com/12359232/how-to-adjust-a-briggs-stratton-governor
The fuel flow solenoid or needle valve it controls may be bad/need adjusted/need cleaning. If your engine has one, it is on the bottom of the fuel bowl on the carburetor. It will have a wire running to it, and when you turn on the key, it will make a tiny "click". If you take it off and remove the fuel bowl. and clean it, then put it back on, it may solve your problem.
I had a similar problem with my generator which also has a B/S engine. Found this on you tube which worked very well for me. Hope it does for you. It also cleans the carb at the same time. Feul lines too if you squirt it in the feul filter and hoses.
https://www.youtube.com/watch?v=5AKKuuXUM6I
Aloha, ukeboy57