Assuming the earth to be a sphere of uniform mass density, the...

The acceleration due to gravity with depth is

${g}^{'} = g\left(1 - \dfrac{d}{R}\right)$

The given data is

$W = 200Nd = \dfrac{R}{2}$

Let the weight be at the given depth, $W '$. Hence, the value is

$m{g}^{'} = mg\left(1 - \dfrac{\dfrac{R}{2}}{R}\right) = m\left(\dfrac{g}{2}\right)$

The Weight $W '$ $= \dfrac{W}{2} = \dfrac{200}{2} = 100N$