I don't think there is an easy way to tell the browser not to download something because the connection is slow. Progressive enhancement can work well for giving users a basic page that loads quickly with minimal assets while also downloading heavier content in the background that renders later. That's still different than putting a timer on a request to download the content (which would require JS to detect the slow connection).
If you make a page well it should render quickly under any network condition, slow or fast. As an example, you could try serving pictures quickly by providing a placeholder picture which uses lossy compression to be as small as possible. It could be byte64 encoded so it's served immediately even over a slow connection. Then after the page is rendered, a request could go out to download the 0.5Mb image and a CSS transition could fade the image in over the placeholder. People on fast connections wouldn't notice a change because it would load right away, while people on a 40kbit 2G connection would be OK with your page too.
The requests to download larger content will still go out over a slow connection but the user won't suffer having to sit through seconds of rendering. Maybe similar to how people have done mobile-first responsive design, people could try doing slow-first design. Get everything out of the critical rendering path and progressively enhance the page later.
If you make a page well it should render quickly under any network condition, slow or fast. As an example, you could try serving pictures quickly by providing a placeholder picture which uses lossy compression to be as small as possible. It could be byte64 encoded so it's served immediately even over a slow connection. Then after the page is rendered, a request could go out to download the 0.5Mb image and a CSS transition could fade the image in over the placeholder. People on fast connections wouldn't notice a change because it would load right away, while people on a 40kbit 2G connection would be OK with your page too.
The requests to download larger content will still go out over a slow connection but the user won't suffer having to sit through seconds of rendering. Maybe similar to how people have done mobile-first responsive design, people could try doing slow-first design. Get everything out of the critical rendering path and progressively enhance the page later.