How can a project realistically tell if a contributor used an open-weight model and self hosted it without it being a de facto ban on AI for anyone not heavily involved in the project?

Open-weight models are still giving up control. For one, all LLM outputs are generally recognized to not be copy writable which undermines copy-left license. Additionally, unlike open source software it's a lot harder to look at what represented in these models. A model can easily be designed to make specific plausible mistake as intentional backdoors, act worse on tasks relevant to an industry a country / maker cares about (like Fable has been designed), etc.