Issue as Dougie pointed out, payload can be gone before you even hook up a trailer. If the rig is at gvw before hooking up a trailer, you have NO trailer capacity! My family of 6 was a bit heavier than dougie, when my 4 kids were adult size teens, we pushed teh scales into the 1200 lb range. Pretty much putting his burb at gvwr BEFORE adding the 600-700 lbs of hw of our trailer. Not to mention the two alaskan malamutes and crates in the bed. Sometimes a canoe, 3500wt generator, 6 bikes, gear for the canoe. It was not uncommon for my CC K3500 to be in the 9-9500 lb range, and it weighed 6600 empty! so 3000 lbs added to my truck, and I was only pulling a 6500lb trailer with up to about 750 lbs of hw depending how it was loaded for what type of trip etc!
Here is a pic of my 88 ext cab, but had the same trailer behind a 96 CC! you can see my sons at age 6 or so, the dog crates, did not have teh canoe, but add a rack, tool box etc......adds a few lbs!

Reality is, if you talk tow capacity, you need to discuss payload! as you can not have one, with out the other! Kinda like HP and torque. For our motors, you can not go forward with out both!
marty