Thank you masterxeon1001, proxe, and team!
https://www.youtube.com/user/masterxeon1001/videos
custombevelprofile001.blend
custombevelprofile002.blend
Adjust segments.
Adjust strength.
[Q] [CTRL+Mark] for Vertex Group Bevels.
[Q] [B] [SHIFT+P] to cycle custom profiles.
Warning: Use only AUTO and VECTOR points. FREE and ALIGN points (= split and continuous Bezier handles) are not exposed in the Blender API and not saved to JSON.
Tip:
CTRL drag profile points for 0.5 units of grid movement.
SHIFT for precise movement.
X to delete a point.
G to move points (X, Y)