The Bevel Mod worked fine for the top buttons. But didn't work for any other edges well. I made the shape twice and still same result. If I try to bevel any other edges, it gets rid of the button bevel weight effect.
You can post screenshots so we can see what is going on better, because there can be multiple things gone wrong.
But the usual suspects are, select everything and M to merge by distance, because you may have double vertices.
You can try unchecking clamp overlap in the Bevel modifier.
Apply the scale of your object.
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).