I'll take the gravitational constant G to be 6.67x10^-11 in this. I will also be using the mass of the earth as 5.972x10^24 (there might be a way to solve this without knowing the mass of the Earth but it has escaped me, if anyone wants to help me out on this then feel free).
We can calculate the gravity of the earth at the distance above it using
g=mG/r^2
Substituting in, we get
g=(5.972x10^24)x(6.67x10^-11)/(6380000+8960000)^2
=1.69 to 3sf
We also know that w=mg, so the weight of the astronaut is w=76x1.69=128.44N = 128N to 3sf
