Why does a falling object have no weight?

Every body on this earth is attracted by the gravitational pull of the earth. A freely falling object has weight W=mg, where W-weight, m-mass of the object and g-acceleration produced due to the earth’s gravity. An object kept in a lift which falls freely, weighs zero on the weighing machine, but its actual weight is still mg. This happens because the normal reaction force exerted on the object in the lift is equal to zero, and normal force equals to mg, which in turn equals the weight of the object.