Overall weight and bike stability?

Bike stability is mostly about frame geometry, a couple of pounds of bike weight won't make a difference you could feel, except that heavier wheels will help steady a bike. Big heavy riders don't get pushed around as much by the wind as smaller riders do. Keeping a low, aerodynamic position helps in crosswinds, and using wheels with low profile rims is also beneficial.

There is not much you can do, a motorcyclist will even have problems with 30 mph cross winds. More weight will just create more surface area for the wind to push you around. All you can do is wear clothing that won't fuff in the wind and go slower when you have to.

Less surface area means less area to push. Think sails on sail boats.

The stability of both motorcycles and bicycles has nothing to do with weight but rather the gyroscopic effect of the wheels. Take your wheel and spin it while holding onto the axle. What you'll notice is that it is hard to change direction. Another example is a top spinning likes to stay upright.

bob is right

ironically 'aero' rims that have lower wind resistance, also have the worst reaction to crosswinds

[[they have a wider profile so a crosswind catches them more]]

wle