"Open weights" is for the most part a term that is meaningless besides being technically able to run it on your own hardware.
I don't think we have a proper term for what you are reaching for, and proper open-source models (training, training-data, etc. being fully open) are scarce.
> I don't think we have a proper term for what you are reaching for, and proper open-source models (training, training-data, etc. being fully open) are scarce.
I think you're very much right that we don't have a "brand" with either the same kind of institutional backing as terms like "open-source" and "free software" or a wealth of examples to point to.