Gravity and Altitude

Your weight is the Earth's pull on you. Set $\relax mg$ equal to the law of gravitation, and your own mass cancels:

$$g = \frac{GM}{r^2}$$

At the surface, $r$ is the Earth's radius and $g = 9.8\ \mathrm{m/s^2}$.

$g$ falls with the square of the distance from the centre: $\relax r = R + h$. Twice as far from the centre, a quarter of the pull.

Twice as far from the centre, a quarter of the pull.