Is it valid to say this is the "weight" of the moon?

I would have assumed such measurements would deal exclusively with the moon's mass.

Are the two terms used interchangeably in this context? (honest question, I really have no idea)

I'm using them interchangeably here, but you're right, it was sloppy - I should have said mass. (They're only equivalent on Earth, and even there a given mass's weight changes based on where you are!)