For 16 GB SSD with 4 GBs of RAM (which is what most Chromebooks used to be), you will need Debian with XFce, with 2 GB of swap partition. Nothing else will either fit, or work properly. I have given away 3 such laptops to friends with that setup (Arch might fit ok too, but because I was giving it to friends, Debian was easier to work with). After installing the v12 Bookworm Debian OS, with libreoffice, a couple of simple games (e.g. solitaire), Gimp, and that 2 gb swap partition, I was left with 5 GB free space. I had to occasionally do sudo apt autoremove to make sure the space wasn't eaten away, but overall, it stayed steady (dh -h will give you that info). With Trixie, you might end up with 4 GBs of free space, as it's bigger. Bookworm has updates until 2029.

Maybe you can have a look at PostmarketOS, depending on the specific model your Chromebook is. They support some Chromebooks.

I have 3 old Chromebooks (2gb/4gb ram and 16gb/32gb storage) and I run MX with XFCE which runs like a dream. Previously I used Arch with KDE which also ran smoothly enough which surprised me. One thing worth doing with whichever distro/DE you choose, remove all the software you won't use and it makes a huge difference!

I used to use Arch + KDE on a device with only 32 gb of storage space. I used BTRFS and transparent compression, and I got the actual Arch Linux install compressed down into 6 gb (where it would have been 10 gb uncompressed).

Try chimera Linux, it is very lightweight (but also depends on the desktop environment)

When you say memory, do you mean RAM or do you mean disk space?

puppy linux

OP, got some specs? It will make it easier for us to give good suggestions. Thanks in advance!

Fedora + sway worked well on my C730 with4gb ram 15gb disk.

i'd just use debian with something like wmaker/icewm/jwm/lxde

I've been distro-hopping on a 2018 cheapo Chromebook for about a year. So far, I've tried Debian (Bookworm) with XFCE, AntiX, PeppermintOS, and now ARCH with Sway. None of the first three were particularly snappy, but they were all running full desktop environments. With Arch/Sway, I'm running about as light as I can get: no login manager, only 441 packages installed. Web browser is Helium. It's early yet, but I think it does feel a little faster--most of the time. Helium still takes a few seconds to load, for example.

Running bare Arch is a bit extreme, but I think the real difference probably comes down to using a WM instead of a full DE. Sway is pretty light, and from what I could find, Wayland is supposed to be a little lighter/quicker than X11, but if toy want to go that way, you could use i3. Configuration from scratch can be a bit intimidating, but I looked online for shared dotfiles I liked and customized from there.

Good luck! Hope it goes all and is a fun experiment!

My specs: Astronaut (rev 3) Chromebook. Intel Celeron N3350 dual core @ 2.4 GHz with Intel HD Graphics 500 integrated graphics, 4 GB RAM, 32 GB eMMC storage.

I would go with debian with a light weight desktop. If you have issues after that maybe puppy Linux?