System Information
Operating system: Windows-7-6.1.7601-SP1 64 Bits
Graphics card: GeForce GTX 980/PCIe/SSE2 NVIDIA Corporation 4.5.0 NVIDIA 446.14

Blender Version
Broken: version: 2.91.0, branch: master, commit date: 2020-11-25 08:34, hash: rB0f45cab862b8
Worked: unknown

Short description of error
Basically if your vertex group "Group" is assigned at value 0.49 or lower the modifier does nothing. Values at 0.5 or above will be beveled as 1.0. So it seems to round up and down / true or false.

I am not sure if this is intended, but wouldnt it make more sense to use the Vertex Groups assigned values to control the Bevel width as well? The Solidify Modifier works like this, for comparison.

This allows to handle different bevel widths similar to the Edge Data variant (Weight). Sometimes I use two or more Bevel layers with different profiles for example. Since there is only one Edge Data available the vertex group method is the next best thing and such a feature would be very handy to avoid making more modifiers and vertex groups for control.

Exact steps for others to reproduce the error

[Based on the default startup or an attached .blend file (as simple as possible)]