But one CAN see the difference!

- While DOF at f/2.8 vs f/4 might be so small in shallowness as to be difficult to assess (e.g. 2' vs. 2.8' DOF at 100' shooting distance),
- if you compare the two images side by side, the greater degree of out-of-focus blur in the shot at the wider aperture can be differentiated. This graph portrays the quantitative difference...
I think we are mixing a couple of issues.
My main point was that unless you intend to shoot at 2.8, you might as well buy an f/4.0 lens and make do with a higher ISO image in those rare instances when one needs the extra light. Yes, the images with f/2.8 and f/4.0 with a bump in ISO would be different, but at apertures >=4.0, they wouldn't be. I'm on my second f/4.o 70-200 and wouldn't consider changing to a f/2.8. One reason is cost. The other is the OP's point: weight. In the case of the new Canon RF 80-200 lenses, the difference is 375g. It was bigger with the EF line, I think.
For the cases where one might shoot at f/2.8, background blur is only one difference. Another is shallower DOF at f/2.8. Speaking personally, I virtually never want shallower DOF than I get at f/4.0 when using a telephoto lens, but that's a matter of personal preference and shooting style.

