350km above the earth is 6378+350=6728km above the centre.
500km above the earth is 6878km above the centre.
If the gravitational force varies inversely with distance from the centre of gravity, the ratio 6728/6878=0.9782 approx. So gravity would be reduced by this factor: 0.9782×2.7×10¹²=2.64×10¹²N approx.
If the force varies inversely as the square of the distance (and I think that’s what applies here) then we need the ratio of their squares: (6728/6878)²=0.9569 approx.
So gravity would be reduced by this factor: 0.9569×2.7×10¹²=2.58×10¹²N approx.