When you run a chromium in headless mode it doesn't make the browser any lighter. I think what the OP means is that you need to have a browser with the most important JS and CSS functionality to render modern websites, but without all the junk on top of it.

qutebrowser and nyxt would fit the bill better. to be honest I feel like nyxt is really cool, but I'm not sure if choosing a lisp was the right idea.

You can install Carbonyl in a VPS and use my Carbonyl Terminal (https://github.com/niutech/carbonyl-terminal) as a thin client for it.

qutebrowser binary is 424MB (on macOS, at least). Is that considered light?

Well my (un-googled) Chromium installation takes up 254MB, and I use that as my "big/corporate" browser so I would definitely not consider that light.

qutebrowser uses a qt-webengine library in the background, which is also basically a full chromium rendering engine, where not all features are exposed to the UI. It's only light in terms of UI. Just like a headless Chromium is only light on the UI side of things.

I tried using palemoon a few years ago, but many web pages just didn't work at all. I wonder if that's changed?

Check out yourself, the latest release was 2 weeks ago: https://www.palemoon.org/releasenotes.shtml

There even was elinks that used svgalib instead of X.

So one could use it on a machine that did not even have any desktop enviroment installed.

This was Links, not Elinks: https://en.wikipedia.org/wiki/Links_%28web_browser%29