The weight of the body at the centre of earth will be zero because g - 0. The weight of the body increases in moving from the centre to the surface of earth and becomes maximum at the surface of earth.
In moving above the surface of earth, the weight of body will decrease (due to decrease in g) and at one place, where the gravitational attractions of earth and moon are equal and opposite, the weight will become zero.
Beyond this up to moon, the gravitational attraction of the moon becomes prominent so the weight will increase.