Do you know if it gravity fed or has the little fuel pump on the side, most likely not gravity since it's a B&S, I think that most gravity feeds are Techumse motors. If it has the pump it will probably have about three screws and a fuel line going into it. If you take that out and look at it is a small flexible plunger type pump that shaft hits and it just goes back and forth to pump the fuel to the carb from the tank. Check the pump mechanism and make sure there are no holes or tears in the little pump piece. They used to look like a paper style diaphram. I'm not sure, but I don't remember seeing to many newer mowers that have the float bowl any longer but it may have one.
Worth checking out if you feel like messing with it. I used to have a neighbor many years ago when I was stationed in Oklahoma that worked on mowers and stuff as a hobby. He got me into it for a while but it was too much like work since I was a mechanic on the flightline at the time.