>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.

Anybody calling SQLite "source available" is mistaken. Are you sure they weren't confusing "source available" with "open core" (Open Source + proprietary add-ons)? SQLite's source code is public domain, which meets the Open Source Definition and is true Open Source. But they also sell proprietary add-ons to fund its development:

https://sqlite.org/prosupport.html

Honestly, I think "source available" is used pretty consistently, and if someone said "weights available" I would immediately understand what they mean.

No one calls SQLite "source available", and if they do, they're doing it more as a protest of their development model than being serious.