Question

The weight of a body will be half its weight on the surface of earth when the distance above the surface of the earth is nearly

Answer 1

According to Newton the force of gravity falls off as the square the distance of the bodies that are attracted to each other.
Your origanal distance from the centre of the Earth when you are on the surface is 6378.1 Km, if you wish to reduce the attraction to half what it is at the surface you must increase this distance to square root 2 times what it was hence you must be 2641.9 Km above the surface.
This attractive force will only be apparent as weight if you are supported on a solid surface if you were orbiting in a satelite you would have no sensation of weight.