This Forum could use a sticky on determining camper weight.
In any case using the manufacturer's specs can lead to grossly underestimating the actual weight. First manufacturer's specs often do not include typical accessories such as an A/C unit, microwave, awnings, etc. Next, many users also add their own mods and accessories. Those might include solar and/or generator, an upgraded and often very heavy foam mattress, steps, additional battery, etc. It is also easy to forget about mods needed to carry the camper. Tiedowns, fastguns, bed mat, SuperSprings/airbags/swaybar or other suspension mods can total a lot more than the weight that is saved by removing the tailgate. At this point it is necessary to add another 1000#, usually referred to as personal items. That seems high but often is an underestimation. This category includes food. A couple of weeks supply and a loaded refrigerator can add several hundred pounds. Also included are clothing, camera/computer/hobby gear, cleaning supplies, toiletries, bedding, cooking gear/plates/flatware/etc, tools, air compressor, lawn chairs, leveling blocks, BBQ grill, and a host of other items we often forget to include. The 1000# estimate needs to be increased due to any special, heavy items some campers bring such as zero gravity chairs, screen house, extra tools, firewood, bicycles and rack, etc.
Also be aware that almost every item listed will be carried by the rear axle, wheels, and tires. The weak links are the wheels and especially the tires. Depending on tire size the load capacity is likely to be 3200-3750 each for a total of 6400-7500. The truck itself is likely to have an axle weight of 3200-3500#, leaving a load capacity of 2900-4300. Again, those maximum weight estimates are based on tires alone. Personally I would like at least a little safety margin. Tires get old and abused with use and especially if take down gravel roads and similar, not to mention driving at highway speeds on a hot day.