At least in my last physics class, weight was defined to be the gravitational force of the earth acting on an object. Perhaps you're blown away because you're equating weight and mass?
To be precise, weight is defined as the magnitude of the force one must apply to an object in a gravitational field in order to hold it at rest.
If you're on the moon, the gravitational force of the earth acting on an object is not what matters. It's the gravitational force of the moon that matters.
They're not measuring weight anyway -- they are measuring mass. Maybe I'll write up a blog post with a picture of how mass spectrometry works. It's a fairly common homework problem in intro EM courses anyway.
