Hi Alxander,
“If I try to bevel any other edges, it gets rid of the button bevel weight effect.”
That’s the Clamp Overlap doing its thing. (There are some Vertices close together (maybe even overlapping), forcing the Bevel to be Clamped.)
You should definitely do a Merge By Distance (in Edit Mode) and Apply the Scale (in Object Mode) as Omar mentioned! Then disabling the Clamp Overlap (under Geometry in the Bevel Modifier).
