Here here! Open weights is the term because it's close to open source but everyone thinks everyone else is an idiot and saying the model is downloadable but you can't recreate it is too difficult for our feeble minds to understand. There are actually open source models out there though, with datasets and training code.

I think it has more to do with the fact that there has to be some term to describe the concept of "model which has weights that are openly accessible"

Like, that's just a logical thing to call it. I don't believe anyone is making a judgement on the intelligence of the reader to call it "open weight" when it refers to weights that are openly available.

"Open source" would be a more appropriate term to describe a model which also includes the training source.

Indeed.