HI Cyril,
There are a few things you are doing wrong, you have Clamp Overlap on in the Bevel Modifier, which stops larger Bevel to happen complete, when there is a smaller Bevel somewhere.Purple Vertices (or Edges) are Creased instead of Bevel Weighted (those are close together in the Menu and easily ‘mis-clicked’):

There might be more…
Also have a look at: https://blog.cgcookie.com/top-5-blender-questions-from-the-cg-cookie-community/