The astronaut's weight is not 60 kg anywhere, because kg is a unit of mass, not weight.
If the astronaut's mass is 60 kg, then his weight is (60 kg)x(acceleration of gravity).
That's 588 Newtons on Earth, and 58.8 Newtons on a planet with 1/10 Earth's gravity.
The astronaut's mass of 60 kg goes with her, and doesn't depend on where she is.
