linuxmemes

For me it was arch, as you start literally with only the packages you chose. So you can go as lightweight as you want. You don't even have sudo unless you install it.

There was also some debian image that was barebones and let you just install what you want. But I don't know if they still offer that option.

Then you don't even go for a desktop environment, you can just use a window manager, like i3. It's more lightweight.

The most lightweight I went without going server was with Arch+i3. But having to install everything you need can be tiring, specially because there are many things you don't know you need until you find yourself without them.

It was a little experimental. For a functional thing you can try debian+xfce (though debian ancient packages can be flustrating), I"m generally fine with Linux mint + xfce or mate. It's not the most lightweight you can go. But it's easy to install and lightweight enough that will run in most hardware.