There's already commented that your envelope is too complex. I tried to draw a simpler envelope, but the result was still a mess. The resulted distortion of complex shapes like your text isn't easily predictable.
Drag your text to the Brushes collection and define it to be an Art brush:
In the left there's your text (actually an outline image)
In the middle there's a drawn curve and the new art brush applied to the same curve
In the right the width tool is applied to the curved text image for thicker mid part.
Workaround 2: Make the envelope distortion with warp (=arc) and edit the result with the direct selection tool. Here's one attempt. Your magenta shape was placed under the work, but it's moved aside to show the mesh: