Question

The weight of any object due to the downward force of what?

Answer 1

Isn't it "gravity" this would makes sense because grvaity difines weight

Answer 2

The "weight" of any object IS the force of gravity between the object and the Earth.

The force is always directed "down", because it's always directed toward the center of the Earth, and we call that direction "down" even though it's a different direction in every place.