You change change the line width by using a "Line Style" expression. Specifically, you want to use a tag <Wn> where n is a multiple for the default line width, and must be between 0.5 and 8. I'm not sure how to apply that to your chart, though, and I suspect it applies to the entire line, not to the line segments that I suspect you want.
You may also or instead want to change line color. For example, in a radial chart I built, I used this expression for the line color:
argb(10+245*sqrt("Count")/sqrt(max(total "Count")),0,0,0)
So color of the line here is used as a "thickness", with the sqrt() behaving as if this were a pipe containing the volume and we're looking at that pipe from above. You could do similar with your line width, of course, but in this case I preferred line darkness. Again, I don't see how to apply it to your chart.
But note the use of argb() instead of rgb(), which makes it easier to see overlapping lines, and also allows the density of the lines to build up as they fall on top of each other. I use that more typically for scatter charts, which makes dense regions of the chart show up much better. But it should also work for your chart, where the overlapping lines would build up to a very solid color, while individual lines could be very light. It has the advantage over the other two in that you don't need to rethink how your chart is built. It should work OK with no other changes.
