Question

if earth's mass decreased to one-half its original mass with no change in radius, then your weight would

Answer 1

Because of symmetry the gravitational field of the earth acts as though all of the mass of the earth were centered at the center of the earth - so g = G M / R^2 and W = m g weight of an individual

If the mass (M) had 1/2 of its value the weight would also be halved.