Weightlessness experienced while orbiting the earth in a space-ship is the result of:

Weightlessness experienced while orbiting the Earth in a spaceship is the result of free fall. 

In orbit, a spacecraft is essentially in a continuous state of free fall towards the Earth. This creates the sensation of weightlessness for anything inside the spacecraft, including astronauts and objects. (As in a lift; which is falling freely, we do not feel any weight, because both lift & we fall with the same acceleration). So the astronaut does not feel any weight inside the spacecraft.