What is the max weight an MTB bicycle with a freewheel can handle until it starts putting high stress on the rear axle?
Axles break for various reasons - weight is only one of them. Miss aligned dropouts, flexing in the frame, tension of the QR all play a big part. Different axles with slightly different materials will also have an effect - some are stronger overall, some more brittle, some more prone to fatigue.
As you identified, riding style also affects the axle loading.
While the manufacturers probably put a number on this for their axles, I suspect its very conservatives and more reflective of there policy around warranty and brand value.
As far as regularly breaking freewheel axles, they are known to be weak compared to other options. A freehub wheel will probably solve your problem, but also check your frame dropout alignment.