It is a guess (not the same author) but it'd make sense: weights are machine output so if the output of AI is not under copyright because it is machine output (which seems to be something that is pretty much universally agreed upon), then the same would apply for the weights themselves.
I'm not sure how someone would argue (in good faith) that training on copyrighted materials does not cause the weights to be a derivative of those materials and the output of their AI is not protected under copyright but the part in the middle, the weights, does fall under copyright.
Note that this would be about the weights (i.e. the numbers), not their container.
Photographs are machine output too and are famously subject to copyright. The movie Toy Story is also machine output, but I'm confident Disney is enforcing copyright on that.
The opinion that AI output isn't copyrightable derives from the opinion of the US Copyright Office, which argues that AI output is more like commissioning an artist than like taking a picture. And since the artist isn't human they can't claim copyright for their work.
It's not at all obvious to me that the same argument would hold for the output of AI training. Never mind that the above argument about AI output is just the opinion of some US agency and hasn't been tested in court anywhere in the world.
As mentioned by the other comment, the difference lies in how much human effort was put - something by its nature is not possible to ask in a black and white manner that applies everywhere. But in cases which are close to the extremes, it is easy to answer: even though the Toy Story renders are machine output, these renders are the result of a lot of human effort by the human artists that made the 3D scenes, materials, models, animation sequences, etc for the purpose of being used in those renders. So Disney can claim copyright on that sort of "machine output".
Similarly, claiming copyright on AI output is like claiming copyright on something like `init_state(42, &s); for (int i=0; i < count; i++) output[i] = next_random(&s);`. While there is a bit of (theoretical) effort involved into choosing 42 as a starting input, ultimately you can't really claim copyright on a bunch of random numbers because you chose the initial seed value.
Of course you can claim copyright in the code, but doing the same on the output makes no sense: even the if the idea of owning random numbers isn't absurd enough, consider what would happen if -say- 10000 people did the same thing (and to make things even more clear, what if `init_state` used only 8bits of the given number, therefore making sure that there would be a lot of people ending up with the same numbers).
AI is essentially `init_state` and `next_random`, just with more involved algorithms than a random number generator.
A photograph is often subject to copyright - but there's actually some nuance here; some countries also require a certain level of creative input by a human.
Areas of dispute include photographs of famous paintings (is it more in the character of a photocopy?), photographs taken by animals (does the human get copyright if they deliberately created the situation where the animal would take a photograph?), and videos taken automatically (can a CCTV video have an author?)
