I don't quite get what's going on. I tried everything: applied rotation, scale, tried re-making the geometry, and nothing works. Could it be that a slight misplacement of a vertex causes such a dramatic change in bevel? It makes no sense. This was created from being mirrored, but it won't apply right. I tried all modes, which I will show below. There is only one that works, but since it doesn't apply it evenly to the bottom portion, I cannot use it as it destroys the top. I need this in order to get the profiling right (otherwise it shows an ugly, impartial application which I demonstrate below as well).
Here are the different types of modes of bevel that I tried (note that they're exaggerated to show how they are unevenly applied).