Lightweight Linux Distros

Unfortunately I don't have a solid suggestion for your list. Personally I use Debian for everything. If I need lightweight, I just do a minimalist commandline install and install fluxbox (usually - or I have also used openbox). If resources aren't an issue, I do a default (Gnome) install.

I did previously use Bodhi Linux which is relatively light weight. But as it's based on Ubuntu, I found that a commandline Debian with fluxbox installed was much lighter.

My son runs Arch Linux. It's quite a different distro to Debian (probably lighter by default), but is somewhat similar in the way that you can build an extremely lightweight system by choosing the right components.