The edges of the paper are "feathered" to make them thinner and the paper is wider than the inner width of the spool. Therefore, on winding the paper forms a black barrier against the edge of the spool to prevent light leaks from the edge inward. It also tends to keep the paper wound more tightly to prevent unwinding when you break the seal or when you take out a used roll.
That is as much explanation as I have been able to dig up. I have no idea how it is done or what the extra width is, nor do I know the thickness at the edge compared to the middle.