The easy way to adjust the thickness of a line surrounding an Inverse Hull Method object is to use a vertex group to control the solidify modifier. The strength of the vertex group is adjusted by weight painting. After you have set up your inverse hull, go to the vertex tab and add a new vertex group by clicking on the plus sign.
It's a good idea to give the vertex group a name like "edge thickness" if you will be using more than one vertex group. Next, with your object selected and your new vertex group selected, enter "Weight Paint Mode."
While in weight paint mode, blue represents a value of 0 and red represents 1. The object starts out blue and you can draw on the surface. It's useful to know that "f" lets you change the size of the brush (click to accept) and "F" lets you change the strength of the brush.
There are a variety of brush setting available to you, Starting out it's easiest to use the brush presets. Draw, Add, and Subtract are good ones to start with, but you have a wide array of possibilities available to you
After you've made some changes, go back to object mode. In the modifiers tab add your vertex group and adjust the Factor to your liking.