These weights normally refer to the actual weight of the servo itself. Specifications for many lightweight foamy models will often list equipment requirements like, "Requires four 9g servos."
A 5 gram or 6 gram servo is an ultralight micro servo used in very small indoor models, where the 9 gram servo is kind of a standard micro servo class for indoor/outdoor electric aircraft. The Hitec HS-55 is kind of the "classic" 9 gram servo, with the HS-45 and HS-35 having been added for lighter weight 5g applications. Digital and metal gear versions are available in most size categories, as well.
With standard servos, the weight is normally irrelevant and the primary concern is the torque output of the servo, that's why you'll see specification like "Requires four standard (43 oz/in) servos" listed. With small electric aircraft, the actual weight of each servo can impact the overall performance of the aircraft, so the weight of the servo is primarily referenced instead.
I hope this illuminates your original question. Good luck and good shopping.