Just go with a Framework 13. Yes it's 13 inch instead of 12 inch. But you will get the best possible Linux laptop out there. And it's also fully repairable and upgradable. I have the latest Framework 13 AMD 7040, yes AMD. And... do not forget to select the new 2.8k display. Allowing for the first time to just select 200% DPI scaling that just works for Linux! So no scaling issues.! https://frame.work/nl/en/products/laptop-diy-13-gen-amd/configuration/new

And select "7640U - 2.8K Display".

Your best bet is an Intel Macbook Air with 11.6" screen from a few years ago. They're even lighter and smaller than the current macbook airs. I have one myself running Linux Mint 22. Just make sure it has 8 GB of RAM (it works with 4 GB too, but you can't have too many tabs open). They sell for $200 refurbished.

You're probably better off looking for hardware to meet your spec requirements and then looking into its Linux support.

GPD might be what you're looking for? https://www.gpd.hk/

X1 Nano:

• narrower than the old 11.6 laptops and slightly taller.
• Higher than 1080 screen due to the taller ratio.
• IPS display
• 0.97kg without charger.
• Thinkpad keyboard and track point.
• strong Linux support

Here is the PSREF for the first generation. They are up to Gen 3 of this line now.

I miss my eeePC

Old used surface pro 3 works great with linux ,hardware still fine and screen is awesome.i own one and run pop os on wayland.

Resolution of screen 2160x1440 12' Intel Core i5-4300U

Thinkpad X280?

LENOVO ThinkPad X280 12.5 LCD Ultrabook - Intel Core i5 (8th Gen) i5-8250U Quad-core (4 Core) 1.60 GHz - 8 GB DDR4 SDRAM - 256 GB SSD - Windows 10 Pro 64-bit (English) - (Renewed) Title https://a.co/d/4ylP22d

If you can stretch to a 13 incher (no pun intended), LG gram might be your best bet. Around 965 gram weight, reasonably priced, can run Linux without any problem.

I use a Samsung Tab 9. Then supplement with a server running VSCode-server and other things. I would prefer Linux, and sometimes use TermuxX11, but it was the best I could come up with.

Minisforum V3 is 12” and less than 1kg.

But it is not quite a laptop, expensive and very powerful - not sure if that suits you.

Linux wise, most of the stuff works (sleep, power profiles, volume buttons, fingerprint reader, face recognition, pen, touchscreen). Things that don't work are automatic rotate/accelerometer.

I'm super happy with it, running arch, doing development and using VMs.

Do your research, but if you can tolerate 13” diagonal screen, the retina intel macbook airs are cheap.

Do you have needs other than Linux compatibility, size and weight and screen resolution?

I have a HP dragonfly g2, 11th gen Intel i5, 16gb of ram, 2.1 lbs, 13” and everything including tent mode works on fedora. I got it on eBay for $275.