The inference engine that I use to run open weight language models is fully free software. The model itself isn't really software in the traditional sense. So calling it ____ware seems inaccurate.
The interpreter is free software. The model is freeware distributed as a binary blob. Code vs. Data is a matter of perspective, but with large neural nets, more than anywhere, it makes no sense to pretend they're plain data. All the computational complexity is in the weights, they're very much code compiled for an unusual architecture (the inference engine).
Regardless of the distinction of code vs data, putting a limit to the number of inferences you can run on a model is essentially the same as using a copyright license on a PNG to limit the number of times you can "run" the PNG with a photo viewer. Is that enforceable? Does it matter? Does the copyright extend to music that my photo viewer generates when I open the image? IANAL but imo, no.
That's typically called freeware, though.