It would seem to me that some confusion is due to sloppy (imprecise) language. The book quotation clearly speaks about roll rate (or intends to), which context is missing from your (Jane's?) OP. For same airspeed reduction of gross weight means lower AoA. I don't understand the book's claim that this increases roll rate. I think the author is confusing roll rate with roll acceleration (the rate of increase of roll rate), and making the tacit assumption that the weight is mainly in the wing, and then reduction of weight means lower inertia in the roll axis.
regards,
HN39