Erik,
Regarding widening the lines all at once, try this, assuming the reference variable for your graph builder is called gb
  _xx = gb << Xpath("//LineSeg");
 _xx << Line Width(3);
 
One method to view one line (one overlay variable) at a time is to add a Local Data Filter.  The only problem I saw was the line and symbol colors are not maintained in the few examples I tried.
 
Attached is a script from Chapter 7 of our book, demonstrating interactive graphs.  This script enhances a graphbuilder plot that has a many level overlay variable,  U. S. states.  The enhancements include:
- a scrollable legend, so the legend box is not taller than the graph, and
 - a mousebox, that hides all but the state of interest; when the mouse is hovered near a state's name in the legend, only that state's curve/points are displayed.
 
I modified the book example with the JSL shown above, that is, it is modified to have wide lines.