I carried an 11' camper on an '07 Chevy 3500 SRW. The camper is about 4,000 pounds loaded. With me, the wife, and the dog in the truck I was about 11,100 pounds going down the road. Sometimes I towed my 4,500 pound boat and trailer behind which probably added about 300 pounds in hitch weight. I never had any problems. I went thousands of miles thru multiple states. The wife even drove a time or two. I did have air bags on the rear and Bilstein shocks. The GVWR was 9,900. I wasn't over axle or tire ratings but the rear was really close.
When we started having kids the regular cab got too small so I upgraded to an '05 crew cab dually. The first time I loaded the camper on I could tell a huge difference in sway just going to the local gas station to get propane. The dually handles it much better. But, the SRW did fine. I had no complaints in the handling department. I regularly had the cruise on 70 mph and one hand on the wheel.