There's a few different levers they can pull, most of them economic & commerce. IEEPA and OFAC sanctions primarily.

They don't have to criminalize the act of downloading open weight models to effectively block access (to foreign open weight models, they have less levers to pull for US based models).

With sanctions and commerce rules though, they can unilaterally prevent all US based businesses from hosting & using them. They will need to be pulled off huggingface, github, gitlab, etc. ISPs could be put on the hook for folks torrenting them as well because technically that could be considered providing serivces to a sanctioned entity. There doesn't need to be monetary exchange.

Likewise, they can use export controls & sanctions to prohibit US companies and individuals from contributing to foreign open source projects as well.

If it went to court, the DOJ would argue that model weights are not speech because it is machine-readable parameters, and not used as a medium of human communication like source code.

Lastly, first amendment rights are unfortunately not absolute since the PATRIOT act. US Gov just has to declare a national security threat and all your rights go out the window.