The gvwr (gross vehicle, or overall) is the total allowable weight. Whatever the door tag says applies to your vehicle, its not going to have a heavier duty axle unless someone put it in it, and if its the heavy duty, its as heavy as it going to be able to handle.
You need to find the curb weight of your truck from specs, or just get it weighed somewhere without anything extra in it, then know the camper weight and do the math. You may get away with going over the rating, but its hard on stuff and may cause problems of you got in a wreck and someone figured out you were overloaded, though Id guess there arent many campers that would overload a heavy duty 3/4 ton.
gawr, (gross axle weight rating) rear axle in particular, is the weight total that can be on that axle. The springs isnt necessarily the issue, its the total package of suspension, axle capability to handle the weight, having little to do with springs, at least compared to how most people look at it, the brakes, wheel lugs, rims, tires that are on it currently. he heavier duty trucks also typically have better grade transmissions, cooling systems including overall larger radiator with more rows of tubes, U joints in the drive line, heavier/larger rear end ring gear and pinions, axles and axle bearings (one of the truly important things). 1/2 ton axles on american trucks are really not very tough, nor are light duty 3/4 tons. The bearings ride right on the axle shafts, weight and wear make the shafts start to lose metal, then the entire shaft and bearings need replaced or the shaft can shear. The 3/4 ton heavy duty with full floater axles and the jap trucks have tapered Timken type bearings and races that are replaceable, and MUCH tougher, and dont require the axle shafts to be replaced when they wear.
I cant recall how many 1/2 ton and light duty 3/4 ton axle shafts ive had replaced, but its a fair pile. One light duty Ford F250 I had, I just replaced the entire rear axle housing and everything with heavy duty parts and was done with all that nonsense for good.
The gooseneck tow rating is higher because the weight is sitting right over the axle, it not cantilevered out off the rear frame and bumper area, though an equalizer hitch helps some in that regard. You are still stuck with the gawr and gvwr, theres just so much actual weight that can ride on the rear axle or the total truck and load weight combined, but it can safely handle more towed weight with the hitch sitting right over the axle. When the weight from a trailer is farther back it affects steering and general handling differently.
Info from Edmunds indicates that the heavy duty truck like yours has a 4045 lb load capability.
https://www.edmunds.com/ford/f-250/1995/features-specs/