21. Astronauts in the orbiting space shuttle want to keep a daily record of their weight. Can you think how they might do it, considering that they are "weightless"?

Yes, the astronaut can keep the record of his weight even if he is weightless. This can be accomplished by creating artificial gravity in spaceship. The principle behind creating artificial gravity is that the spaceship is rotated with some speed about its axis of rotation. The centrifuge acts on the objects inside, including the astronaut, and with no centripetal force, the astronaut is pushed farther from the axis of rotation by the centrifugal force.
Eventually, the centrifugal force is large enough to push the astronaut against the inner surface of the space ship, and the astronaut is no longer weightless.
The rotational speed is adjusted such that the magnitude of centrifugal force acting on the astronaut is equal to the magnitude of gravitational force on the surface of Earth. Therefore, to the astronaut it appears that the gravitational force is acting on him, and he can then choose to measure his weight.