I would take the carburetor off and clean it thoroughly after making sure to clean the tiny orifices with carburetor cleaner and a small wire ( I use twist ties ) and that should help. Usually one of those tiny holes in the carburetor throat under the throttle plate get plugged up and varnished over. You might get lucky with some carburetor cleaner and a small wire bent at a 90 degree to gently poke those holes clear of varnish. Some of those 3.5 Briggs engines have carburetors on top of the gas tank, and others have the float bowl type arrangement with a fuel line going down to it from the tank. On the carb above tank types I clean where the carb bolts to the tank. Take the carb off and check the diaphragm. Sometimes they get old, stiff and won't work well. Sometimes the fuel pickup tube screens are dirty and gummed up. I've replaced several of those type diaphragms this summer. With the float bowl, it gathers water and sediments and doesn't take much to cause an engine to stumble, sputter and quit.
