darkroom - not sure what you're saying there. Any steady wind (cross or not) has absolutely no effect on any aeroplane, from a glider to an A380 to a Space Shuttle, other than to vary its groundspeed and track. It has absolutely no effect on how it flies.
As I said:
size and weight are not factors
Using the shuttle I was attempting to clarify for the OP that even though mass (weight) has SOME effect, it is minimal. Using a rock and an aeroplane would be a better example. A paper aeroplane weight less than a rock. A paper aeroplane will be blown about in windy conditions, a rock will not (Unless it's REALLY windy), BUT a Cessna 172 which is much heavier than the same rock will also be blown about more than the rock in windy conditions. So weight (mass) is NOT a major factor in the effects of wind, cross wind, gusts, turbulence or any other changes in air flow. Shape is far more important.
However momentum (which is affected by weight/mass and speed) does have some affect on the effects of other forces being applied to an object, whether those forces are gravity, propulsion, or wind. It is just that in the case of something designed to fly, the shape has more influence on the effects of wind than does the mass of the object.
@Fly-by-wife, I beg to differ, weather cocking can be seen and felt in flight. It will be about EITHER the point with greatest resistance (as in the wheels when on the ground, or a pivot point in a wind tunnel) OR it will be about the centre of gravity in flight. This is what we experience in turbulent air when the plane pitches or yaws. It is that some parts of the plane will present more drag than others, and thus be affected more - BUT it is absolutely NOT related to weight (mass) or over-all size of the aircraft.