The vimscripts entry for nuweb.vim (which is referred to by the README.md in the GitHub repository) gets into more details about how to install it:
As WEB/CWEB uses *.w, i recoment use *.nw for NUWEB, so some like
au BufNewFile,BufRead *.nw setf nuweb
in filetype.vim will do the trick.
In modern Vim, this is typically accomplished by ...