"In particular, the license states that if one redistributes a program derived from our work, the corresponding modifications of our sources and all information needed to build that program must be made available. Only after explicitly informing Albert Silver (the author of the net in Fat Fritz 2) of a license violation have matching C++ sources, but not the net weights, been made available. Obviously, we condemn the approach taken."
Should I be legally compelled to share the net weights of my trained NN?
If you have a non-GPL license to use and redistribute the data you use to train the neural net, I would imagine not.
Under GPLv3, the answer is explicitly clear: "The output from running a covered work is covered by this License only if the output, given its content, constitutes a covered work."
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.