Can weights be copyrightable?

Licenses are not copyright law, they are contract law. Copyright is automatic and does not require any terms, as long as the work is covered by copyright. Contract law can then override the innate copyright rights (for example to permit people to use your copyrighted works).

If you create something that isn't copyright-able, you can still create a contract which people must agree to in order to use your work. The enforcement/validity of that contract then depends on making sure the user knew about the contract and agreed to it. The way they did that here (just publishing a LICENSE file) could be interpreted as a judge as no confirmation of agreement of contract - depending on if they find a "reasonable" user would have known to look for the file.

Copyright is an automatic protection (meaning you don’t need to register it, like registered trademarks), for certain types of creative works. Contracts are one way to dish out these rights (eg. for a fee).

If you have a work that is not copyrightable, and you give it to people lawfully, then you cannot protect it via copyright.