In your question, when you said "... an astronaut has a mass of 60 kg ...",
you didn't mention where he has that mass ... you only said that he has it.
Clearly, then, his mass doesn't depend on where he is. It's the same mass
everywhere.
His weight, however, does depend on where he is, because the weight of
any object is the gravitational force between the object and something else.
When the 60-kg astronaut is on Earth his weight is 588.4 newtons (132.3 pounds).
When he is on the moon, his weight is 97.4 newtons (21.9 pounds).
