Rate of change of weight near the earth’s surface varies with height ‘h’ as 

Weight of body of mass m at height h from earth's surface is given by 
$\mathrm{w}={\mathrm{mg}}^1=\mathrm{mg}\left(1-\frac{2\mathrm{h}}{\mathrm{R}}\right) \mathrm{where} \mathrm{h}<<\mathrm{R}$
$\therefore \frac{\mathrm{dw}}{\mathrm{dh}}=\frac{\mathrm{d}}{\mathrm{dh}}\left[\mathrm{mg}\left(1-\frac{2\mathrm{h}}{\mathrm{R}}\right)\right]=\frac{\mathrm{mg}\times 2}{\mathrm{R}}= \mathrm{constant}$
so, $\frac{\mathrm{dw}}{\mathrm{dh}}\propto {\mathrm{h}}^0$