It's not independent because if I'm 80kg here, I'm still 80kg on the moon. Because gravity does not affect mass.

If I weigh 160lb on earth I'm told that I would weigh 26lb on the moon.

That makes sense if lb measures force because gravity affects force.

In short, this commonly shared "fact" is consistent with pounds being a unit of force, not of mass.

Or, I suppose, of lb at least sometimes being a unit of force.

If you weigh 160lb on the Earth, you also have 160lb of mass. You would weigh 26lb on the moon and still have 160lb of mass.

I don’t know how to make the point any clearer that there are two units of measurement, both with the same name.

https://en.m.wikipedia.org/wiki/Pound_(force)

https://en.m.wikipedia.org/wiki/Pound_(mass)