I've also heard it used to describe projects that are open source by anyone's measure but have contribution or project governance requirements like for example sqlite.

"Source available" is definitely in much wider use than "weights available" but it's not that common and it's not used consistently at all in my experience.

Weights are different enough from source code I don't find the metaphor useful or compelling. I don't see any value in trying to apply it to a novel subdomain of software engineering, frankly.