With some more experimentation, it looks like part of the factor is the number of Line series that I'm using this way in a chart. If it's a single series with a bunch of points, the gradient line is generally fairly visible (though it still changes width in different scenarios, and I'm not sure why), but if I increase the number of series that I'm using, even if all the points and connections are the same (i.e., using a separate line series for each line connection between successive points), the width of the line drops significantly.
Perhaps there's another way to do what I'm trying to do. Right now I'm graphing a scatter-XY plot of data for historical data, but time is not one of the axes. I want to have the oldest point be a particular color and the newest point be a particular color and all the points in between should grade between those colors; this is the simple part, though it does involve making ~200 different point series. Additionally, I want the same sort of color-grading line connecting the points in chronological order. The simple way to do this is to also use ~200 line series, because a single series will repeat the exact same gradient along each segment, so I need to have only one segment per series. The problem is, apparently the more of these series I create, the thinner my lines get.