I think I win as I'm ~2500lbs over GVWR for my truck! 9200 GVWR and weighed on a CAT scale full of fuel, 4 passengers and camper packed for trip (full water tank empty holding tanks):
Front Axle 4500
Rear Axle 7240
Total 11740
Driven this rig for 8 seasons and it handles awesome when loaded, with all the mods I did it drives like an empty DRW without the camper on it:( You have to do your homework if you're going to exceed OEM limits, for my truck I've spent ~$5.5K aftermkt to make sure it exceeds loads on both axles:
2007 GMC Sierra 2500HD Classic CC 4x4 Diesel SB
AAM rear axle rated at 10400 lbs
front axle GMC load rating 4800 lbs
Cepek Hummer H2 17x8.5 wheels rated at 4500 lbs each: $2K
Nitto Dura Grappler 285/70r17E tires rated at 3750 each: $1K
Supersprings, AirLift air bags: $600
Cognito Leveling kit with Bilstein 5100 shocks: $900
Herculiner bed liner with thick rubber bed mat: $100
Torklift frame mount tie downs: $500
Titan Class V tow beast: $400
Braking is fine as the 2500HD Diesel has grade braking and a GCWR of 22K so I'm 9K below that. Sway is not a problem with the Supersprings, considered a rear sway bar but never felt I've needed it.
If you don't want to go to these extremes then I suggest just making sure you don't exceed GVWR by more than 500lbs and make sure that your rear axle wt is within the limits of the tires and wheels.
I wouldn't do this again but back in 2007 there wasn't a GM 3500 SRW 6.5' bed option as there is today and I needed a SRW for where I camp which is why I sold my old DRW and 11.5 Arctic Fox for something smaller.
Happy camping