How to make a collection of shapes pinch on the ends

Aside from the Envelope functions, I like using a trick involving Art Brushes. If you turn your type object into an Art Brush you can apply it to a curved path and then edit the path to your preferences. The Width tool changes the thickness of a line stroke on different parts of a path. For instance you can make the path thick in the middle and thin on the ends. It will also work with paths that have Art Brush effects applied to them.

As Monika mention try Warp from Envelope or Mesh tool

Carter,

How about this?

1) Type the text (just keep as live Type), then apply Bulge (in the Arch Group under Warp under Effect) and make an Art Brush of it;

2) Create the curve with a 1pt stroke and no fill, then apply the Art Brush from 1).

Click/RightClick to get closer

You might want to check out the envelope function.