Gitea is pretty light on resources so even though it has a extra functionality you don't need it's not really a resource pig. Unlike say, GitLab.
I'm just looking for "website" (read: interface) that list files over HTTPS, with the ability to show nice looking diffs. Some sort of ssh keys(?) to prevent unauthorized access etc.
I have not used it before, but it seems like it follows your requirements (Except auth using SSH keys maybe, but that could be a task for e.g. Nginx)
https://github.com/sitaramc/gitolite
I've not used it personally though, so no idea how well it works in practise.
I just found about "git instaweb" (developed by Git authors, but it's extra OS package) - it works locally, probably what I was looking for (minus the 100% width page layout).
BTW There's Gitblit is someone's fancy hosting Java app.