I doubt very much you're over your actual rear axle's weight limit... most 3/4 and 1 ton SRW axles are rated for at least 11000 lbs now. What limits the RAWR on pickups is the rear tires' load rating (3/4 and 1 ton SRW usually share the same axle, as well as the frame and brakes, they are usually differentiated by an extra leaf spring and higher load rated tires).
Stock tires on 3/4 ton trucks usually are rated for around 3050 lbs, thus the GMC Rear Axle Weight Rating of 6100 lbs or so. If your tires are replaced with higher rated tires, your RAWR (unofficially - because the factory sticker is based on the stock tires the factory installed) also goes up because it's still well within your actual rear axle rating.
I can't tell you it's OK or it's not OK, but most of the 1 ton trucks with higher GVWR are the same truck as a 3/4 ton, except for the tires and perhaps an extra leaf spring, which you can add air bags if your truck sags, as that is all the extra leaf spring would prevent as well, but that won't increase your RAWR, as neither will an extra leaf spring, if your tires are still the limiting factor.
This is not a cover-all post that suggests it encompasses all trucks and all situations... so you need to do some research on your particular situation.