I bet its not as bad as you think. empty the camper and weigh it again. bet it weighs closer to 3000 empty.
I would add ....and all the gear/addons out of or off the truck would give a better shot at how much the TC actual dry vs wet weight.
I see many claim their TC weighs xxxx lbs but their including gear and stuff/necessary junk/etc we carry in or added to the truck.
example;; Two hi-lift jacks/2-3 jerry cans/tow chains/gen set/heavy custom bumpers/etc I've seen on some TC combo's I've seen in CO/UT/NM isn't part of the TC's actual weight but rather how much the combo weighs.