Lightweight distro for a server is nonsense, IMHO. All major distros are made to work as a server (enterprise ones are made primarily for servers), so whichever one you use currently, use it. Debian, Fedora, openSUSE, Arch, whatever.
I use arch.
edit: lol while I am new to arch, I guess I kind of expected people to disagree with me. I was under the impression that stock arch is very lightweight? I know there used to be jokes about "I installed Arch" cause it's supposed to be hard. But I installed Arch on my desktop and server recently, I did the manual install on my desktop and the guided install on my server. Both super straight forward. Plus Arch seems to have some of the best documentation across distros. I don't know why it should not be suggested, unless I am missing something.
From Wikipedia, the free encyclopedia
Linux is a family of open source Unix-like operating systems based on the Linux kernel, an operating system kernel first released on September 17, 1991 by Linus Torvalds. Linux is typically packaged in a Linux distribution (or distro for short).
Distributions include the Linux kernel and supporting system software and libraries, many of which are provided by the GNU Project. Many Linux distributions use the word "Linux" in their name, but the Free Software Foundation uses the name GNU/Linux to emphasize the importance of GNU software, causing some controversy.
Community icon by Alpár-Etele Méder, licensed under CC BY 3.0