How can you explain that air has weight?

Answer 1

Experiments which can prove that air has mass and therefore weight abound, but I'll give a simple thought experiment here which indicates that air must be massive.

Assume that the atmosphere of the earth has some pressure P at the surface of the planet (reasonable, as many homes have barometers which measure just that), and determine what the pressure will be at other altitudes.

Pressure exerts a force proportional to the value P and the surface area A of the face of the volume you are considering out of the volume, this is its definition. If that force is not balanced by another force on the face of that volume then the air will reapportion itself until the forces are balanced, which will lead to a different pressure. If air has no mass then the force of weight does not contribute to the overall force on any volume of air, and it can only be balanced by an equal pressure immediately above it. This is true of any volume of air, not just those at the surface.

Thus we see that if air had no mass then the atmosphere would have to extend throughout all space to remain pressurized at a fixed value. Since this is clearly not the case according to repeated measurements of atmospheric pressure at altitude, as well as being contradicted by the many space missions which have been performed, air must be massive.

Answer 2

yes it does