Answer
Astronauts are weightless because they are in free fall and there is no support force. This is discussed on pages 166-167. The gravitational field of Earth is definitely not zero at that height.
One can calculate g at the approximate height of the ISS.
$$g= G \frac{M_{Earth}}{d^{2}} = (6.67 \times 10^{-11} \frac {N \cdot m^{2}}{kg^{2}}) \frac{(6.0 \times 10^{24} kg)}{((6380 + 400) \times 10^{3} m))^{2}}$$
$$g= 8.7 \frac{m}{s^{2}} $$
This is not zero. If Earth's gravity at that height were zero, the ISS would feel no force, and move in a straight line at constant velocity.
