A common problem. I've been reading all the posts about this, and there are many causes, but I've just found mine. Grit in the bowl under the carb. It's not the load that causes the mower to stall--it's the jiggling over the lawn that disrupts the grit particles so they plug the carb. The mower will run fine standing still on the level because the particles settle to the bottom of the bowl.
I don't buy the stale gas story. I've run old gas in mowers for years, with never a problem. But yesterday I did empty the last of the gas in the can into the mower, probably dumping in several years' accumulation of grit (and it doesn't take much to plug those little carbs). Usually I fill the gas can before it's empty, and the grit stays in the bottom of the gas can.
Moral of the story: Old gas is OK with me, but I'll never again empty the last of the gas can into an engine.