An example of an output constituting a covered work might be that if you use a GPLv3-licensed library to output a timezone database shipped with the library in a JSON format, because the content of the JSON output is itself a derivative of a GPLv3 work, not only an output, it would be covered by the GPLv3.

In order for NN weights to be covered, the weights would need to be in themselves a derivative of a GPLv3-licensed work.

Training a NN on GPLv3 licensed training sets would (IMHO) make it a derivative work, that's what a lot of the Copilot uproar is about.