Hi, thanks for the report.

I can confirm that it works as you describe. I'm not sure on intended behavior, prolly ask @Howard Trickey (howardt)

Only other report I found was:T73028: bevel modifier not working really well with bevel weights

It seems that with a low bevel weight on a single edge of a cube makes it really bulge out.

For reference, I'm guessing the desired behavior is more like this:

Done by first beveling the 2 edges and then using a second bevel modifier with a vertex group of the other edge. I'm not sure how or if this can be done internally though.

@Howard Trickey (howardt)
I've been looking into this, and it looks like a problem with the cube corner special case.

With Special Case	Cube Corner Special Case Off

/bmesh_bevel.c b/source/blender/bmesh/tools/bmesh_bevel.c
index d1ddceb00b0..0d753eca675 100644
--- a/source/blender/bmesh/tools/bmesh_bevel.c
+++ b/source/blender/bmesh/tools/bmesh_bevel.c
@@ -4167,6 +4185,9 @@ static int tri_corner_test(BevelParams *bp, BevVert *bv)
   if (bv->vmesh->count != 3) {
     return 0;
   }
+
+  const float offset = bv->edges[0].offset_l;
+
   totang = 0.0f;
   for (i = 0; i < bv->edgecount; i++) {
     e = &bv->edges[i];
@@ -4178,6 +4199,11 @@ static int tri_corner_test(BevelParams *bp, BevVert *bv)
     else if (absang >= 3.0f * (float)M_PI_4) {
       return -1;
     }
+
+    if (e->is_bev && !compare_ff(e->offset_l, offset, BEVEL_EPSILON)) {
+      return -1;
+    }
+
     totang += ang;
   }
   if (in_plane_e != bv->edgecount - 3) {

But the VMesh has some other issues when using the generic VMesh:

Would you agree that it makes sense to disable the cube-corner special case when the offsets aren't the same on every edge?
That doesn't feel like a complete solution by itself, but I feel like we might be running into the limitations of the ADJ method. Maybe it's time to test out another VMesh method idea I had..

Yes, makes sense to me that the cube-corner case only makes sense if the offsets are the same on every edge.