Weight is the force generated by the gravitational attraction of the earth on the airplane.
We are more familiar with weight than with the other forces acting on an airplane, because each of us have our own weight which we can measure every morning on the bathroom scale. We know when one thing is heavy and when another thing is light. But weight, the gravitational force, is fundamentally different from the aerodynamic forces, lift and drag. Aerodynamic forces are mechanical forces and the airplane has to be in physical contact with the the air which generates the force. The nature of the gravitational force has been studied by scientists for many years and is still being investigated by theoretical physicists.