That function is called “Edge bevel weights.”
In edit mode: ctrl+e -> (something like bevel weights) -> enter a value between zero and one that will serve as a multiplier for the bevel radius for all edges selected.
This is associated with the option in the bevel modifier limit by: weight.
(I may not have the terms right; don’t have Blender in front of me, but what you’re looking for is possible.)
You can use vertex groups to bevel vertices but not edges. It has been a feature request for a while to make it work for edges too, and it will not be very hard to do, but I have prioritized it behind fixing bugs in knife and bevel first. Maybe I’ll get to it this release cycle. If a new developer wants to get their feet wet, this would be an easy first project and I would be happy to review a patch for it.
You should read what people write more carefully but anyhow Howardt has already confirmed that he is aware of the limitation I spoke of so no problem…(in my post I did write about the limitation of bevel weights). weights are acts like a multiplier to the width value so there is a limit to how sharp or loose it can make a bevel plus it has no effect on the segments of a bevel IIRC.
I saw this in the “Did you see the latest awesome…” thread and said thanks there but I will say thanks again here. I really appreciate this new addition to the modifier. I downloaded a build and will be testing it out this evening.