Heck my trans made it to 145k before I lost reverse, LOL! As KDJ pointed out you need to consider how many people in the burb. 8000 is the max tow rating , and each passenger subtracts from that. Also factoring into the payload limit of the burb is the tongue weight of the trailer. A 6500 lb loaded trailer with 13% tongue weight will add 845 lbs to the burb on the hitch. If you are a family of 4, I would stay around 4500-5000 dry weight, that will keep you in the 5500-6000 loaded weight range and you should be OK.
Regarding the receiver, the design on the 00-07 GM trucks is awful, mine was one that broke. It seems that the failures were limited to those towing heavy with HD weight distribution hitch. Most of the HD trucks tow 5ers so it was never an issue. My TT at 8500-9000 lbs (depending on how it's loaded) put too much stress on the receiver and it twisted off. At your weight you should be fine. One symptom of it starting to fail is not being able to level the traiuler with the same WD settings on the hitch. The receiver takes the "wind up" on the WD instead of using the torsion in the hitch to level the truck and trailer.
Over all these are good machines...if yours has spent any time by the seashore keep an eye on the brake lines for corrosion.