Why is it more correct to refer to the mass of a body than to its weight?

Mass is the AMOUNT OF MATTER in a body.

Weight is the FORCE DUE TO GRAVITY on a body.

Gravity acts as an attractive force between two bodies which have mass, and increases in magnitude as a body's mass increases. The Earth's gravity accelerates objects at a rate of about 9.81 meters per second per second, or meters per second squared. This is true for all bodies in the gravitational field, regardless of mass or weight; if an object falls faster or slower on Earth it is due primarily to air resistance.

According to Newton's Second Law, F=ma, or Force equals Mass times Acceleration. In the case of Weight, W=mg, or Weight equals Mass times Gravity. Weight is expressed in Newtons or Pounds, whereas mass is expressed in Kilograms or Slugs (that's metric and English systems respectively)

As to whether it is more correct to use mass or weight, that depends on the application. If you are trying to determine the safe load for a structure, you definitely need to have the force being exerted by the bodies above your structure, so you need to know the weight. If you are doing chemistry, mass is far more important than weight when you are trying to get a certain number of moles of a material, especially since weight VARIES depending on where you are on the planet; you actually weigh more the closer you are to the equator because the earth is not a perfect sphere.

So weight is the force acting on a body depending on what is next to it (planet) and mass is the amount of matter in a body.