If someone wants to release weights but attach a no commercial license to it I'm somewhat fine with that. I won't be able to sell it behind a shallow API but I'll be able to use the output of the model (that can't be prohibited) and sell that or do whatever I like with it. It's not as ideal as CC0 but I'm ok with the compromise.
(Maybe it's wishful thinking. But, precisely. My analogy would be: you can't run Visual C++ for commercial purposes without a valid licence, even though (ignoring linking against the runtime), the license of a compiler doesn't affect the licence of the output.
If weights are copyrightable, then you need permission to copy them into computer memory/run them, just like any application.