A weight of a mass is given by m*g, where g = 9.81 m/s^2. At what distance from the Earth does the weight become half.

The weight of a an object is the force exerted on the
object by the gravitational pull of the Earth.

If the mass
of the Earth is taken as Me, the radius of the Earth is Re; we get the gravitational
force between the Earth and an object of mass m as

F =
G*Me*m/ Re^2

We have G*Me/Re^2 =
9.81

For the force to become half while G, Me and m are
constant, the distance of the object from the center of the Earth has to be
increased.

Let the distance be
D

G*Me/ (Re + D) ^2 = 9.81 /
2

=> 9.81* Re^2 / (Re + D) ^2 = 9.81 /
2

=> (Re + D) ^2 = 2* Re
^2

=> Re + D = sqrt 2 *
Re

Taking the radius of the Earth as 6300
km

=> D = Re*(sqrt 2 -
1)

=> D = 6300(sqrt 2 -
1)

=> D = 2600
(approximately)

The weight is half
approximately 2600 km away from the surface.