"The engine (Briggs & Stratton 2.75 horsepower, the label on the engine says) on my lawnmower is acting up, "
Define acting up? Its been my experience(and I'm not a fan of B&S) that most of the time running problems are a result of failed carburetor gaskets. Most of the B&S engines I've seen have this odd 'pump' gasket arrangement, the carb sits on top of the tank, so you have to have a method to pull the fuel upwards. The two gaskets on the tank are the usual culprit although sometimes you can get away with tightening the screws a bit.
It really says something to me when I walk into the lawnmower parts shop with the gasket in hand, and the lady sees me coming, doesn't even need a part number...and goes behind the counter to get what I need. Same goes for that total piece of crap primer bulb that B&S uses. Good for about a year, tops, before the rubber crumbles and plugs up the fuel passages in the carb(ask me how I know...). And with the fuel BELOW the carb, a primer button is pretty much mandatory to get at least some fuel into the intake to get the 'pump gasket' system working.
I'd much rather have an old-fashioned style setup, fuel up high, float bowl carb below, and a choke lever. It just seems more robust to me....
Best,
Chris