Mike,
As you've noted as you land when the wind changes direction or speed the aircraft feels the effects of changes in forces on its surfaces.
A heavy aircraft will have momentum in its favour, obviously, however and if you have the same aircraft landing with different weights, you'll see a SMALL difference between the two loadings.
However if you have two aircraft with the exact same weight, but one of them has a tail surface that is 4 times the size of the other, you will see a DRASTIC difference between the two aircraft.
Mass (weight) DOES have an effect on the affects of wind, however shape has a much greater effect.