I haven't read all the "weightless" posts, just some of them. I have for a long
time (decades) refused to use weight as mg or anything of the sort. I just
speak of the gravitational force. My force diagrams don't have W, just mg as
the gravitational force, with an arrow over the g. (The magnitude of the g
vector is usually, but not always, the value 9.8 N/kg at the earth's surface; I
define it more generally.)
I never use the term "weight" either. I do point out maybe once that weight is
what a scale measures, and is thus the normal force on an object by the scale
(or whatever). It's mg only for non-accelerating objects. Anyway, then, an
astronaut in a spaceship in a circular satellite orbit really is "weightless."
It is so easy to teach physics never using "weight" but using "gravitational
force" instead and putting mg on your diagrams, not W. It sure avoids a lot of
difficulties.
Needless to say, I quit using textbooks years ago for introductory algebra- or
calculus-based courses. But there were other reasons for that, which I may
discuss in another post after Thanksgiving.