I'll star a repo when I want to add it to my "favourite" or "interesting" repos - they are all listed under "Your stars". Is there a better way of achieving the same?
I like that it lets me open files without JavaScript enabled and search the code without logging in. I still use GitHub.com to read the issues on a couple repos though.
Example of what gitweb looks like: https://sourceware.org/git/ - There's also cgit which is similar: https://git.kernel.org/