We know, Weight (w) = Mass(m) * Acceleration due to gravity(g)
If the weight of a body is 0, either the mass or the gravitational acceleration is 0, or both are 0. But, mass of a body can never be 0. Thus the gravitational acceleration has to be 0.
But a body during free fall possesses acceleration as well as mass.
So, why is a freely-falling body weightless ?