While not directly analogous, people often think "it's just math" or "it's just numbers" and therefore claim their use is ok. I would encourage those people to read about illegal numbers: https://en.m.wikipedia.org/wiki/Illegal_number
I think you could replace "weights" with other things that you probably would want restricted (eg private keys).
My point is exactly that: just because something is the result of some fixed mathematical process plus randomness does not mean there's no nuance and it's always ok to share/publish.