You are rounding a lot of things off, I would not do that but look at actual amounts and don't trust guessing/assumptions. It is sort of like guessing what is in your checking account, without doing the actual math.
A few things. You mentioned your truck is a 2003, what tires do you have on the truck? Often, the weakest link will be your tires and rims.
Next, actual weights of your truck would answer your question. Often we have new Truck Camper owners arrive here to ask questions to receive affirmation to their needs. If so you have arrived at the wrong place. This group wants you to be safe, as well others that travel on the roads that you travel on, as well.
Another important factor is your estimated personal stuff weights. The figure that has been the approved amount, after many years of discussion here, is a firm #1,000 lbs.
Also, don't go by what an individual tells you what the camper weighs, especially if they are selling the camper.
Don't believe the sticker on the side of the camper, as that is often not even close to what the Truck Camper actually weighs. Go weigh the camper, if available, or if your margins are close with the available carrying capacity of your truck. Having a comfortable/safe truck laden with a Truck Camper is a wonderful feeling.
So;
What are the actual numbers on the door pillar tag?
What is the weight of your truck, from a recent scale weight?
What is the camper you are looking at (most of us can get you a better idea what the expected wet weight of that camper will be)?
What is the cargo capacity of the current tires you have on your truck?
Do you have the OEM Rims on your truck? (If not what is the capacity of the current rims?)
By all means, have fun!
b
08 F550-4X4-CC-6.4L Dsl-206"WB GVWR17,950#
09 Lance 1191
1,560wSolar~10-6vGC2-1,160AmpH~Tri-Star-Two(2)60/MPPT~Xantrex 2000W
300wSolar~2-6vAGM-300AmpH~Tri-Star45/MPPT~Xantrex 1500W
16 BMW R1200GSW Adventure
16 KTM 500 EXC
06 Honda CRF450X
09 Haulmark Trlr