The US doesn't have database copyright, but some countries, including the entire European Union, do.[1]
That's different from creative works where it's implausible to claim that you created the same work independently of someone else.
I suspect that part of the arguing this out in court will be making those economic arguments as part of an attempt to extend copyright protection to model weights - but that is a separate issue from if they are protected currently.
Part of the economic argument for copyright is to encourage the investment of time into producing new works, so it may be a persuasive argument for extending protection. Although (relatively) recent history suggests that persuasive argument is not as powerful as giant wads of cold hard cash in extending copyright coverage.