Mechanic Mark is probably more on target than I am, but I did want to relay one specific experience with my LawnBoy bogging down just as you have described. Heavy grass, or engaging the self drive would bog it down. Heavy grass and engaging the rear wheel drive combined and it would stall out.
After a lot of fiddling I realized that the Governor Vane was not freely pivoting. Crud had built up beneath the Vane pivot point on the Carb and was not allowing it to move freely, thus no Governing of the engine. Carb Cleaner and Liquid Wrench sprayed into the Governor Vane Pivot Point finally fixed the problem after a season of issues with bogging down.