Although the Earth’s gravity has a lesser effect on an astronaut orbiting the Earth in a spaceship than on a person on the surface of the Earth, this is not the reason why an astronaut experiences weightlessness.
The space shuttle, International Space Station and most other manned vehicles don’t get that far from the Earth. The Earth’s gravitational attraction at those altitudes is only about 11% less than it is at the Earth’s surface.
The astronaut, the spaceship and everything inside it are falling towards the Earth. The reason why the astronaut doesn’t go splat is because the Earth is curved and the astronaut, the spaceship and everything inside it are moving “sideways” fast enough that, as they fall towards the Earth, the surface of the Earth curves away from them. They are always falling towards the Earth, but they never get there.
Quoted text by Steve Gagnon via Jefferson Lab.