Jeff,
If you want to stay under gross truck weight and payload weights then subtract the empty truck weight from the gross weight. That is your allowable weight for fuel, people, tools, dogs, and the camper. In your case that weight is around 2500 pounds. Most truck camper owners use about 500-1000 pounds as a rule of thumb for water and stuff if the manufacturer does not include water, propane and batteries in their weights. Adding overload spring bumpers, air bags, tires, shocks etc. does not increase the gross weight of the truck but it does help with the camper ride. The axle gross weights are never to be exceeded and are always higher combined than the truck's gross weight. If you plan to tow any trailer the tongue weight is deducted from the truck's payload. Folks towing a trailer and hauling a truck camper usually opt for a one ton and a one ton dually is almost required for campers that are around 4000 pounds and also towing much of any trailer. From your numbers you have space in your rear axle rating of about 3150 pounds, not much as it relates to the larger truck campers. And that 3150 pounds also includes people and stuff inside the truck.
Many on the TC forums will go over GVWR slightly, like less than 10 percent, but I know of none that are willing to go over any axle gross weight.