Are weights even copyrightable under US law? It seems like they'd be the output of an automatic process (the training program) the same way the art/text produced by AI models is, which to my understanding makes them not copyrightable material.
Compression, even lossy compression, doesn't remove copyright. Whether this is more like compression or a more "transformative use" is something the courts will have to decide someday.
It might be a good time to reread What Color Are Your Bits:
There is a lot of manual process involved such as writing training scripts, scarping and processing training data, choosing the best weights among several runs, and spending lots of costly computation. Maybe these should make it copyrightable.