1968lbs is "just for the cab" WOW! Don't know what to say...
The Tire and Loading Information sticker is for THAT SPECIFIC truck model and package as equipped as it rolls off the assembly line. Includes full fuel, but no driver or passengers. It is required by law to be within a few pounds of the actual weight if you randomly picked one and weigh it. The sticker states exactly "The Combined Weight of Occupants and Cargo Should Not Exceed XXXX" That means EVERYTHING put in and on the truck counts against that number. If the dealer or aftermarket upfitter adds anything more than a few pounds they are legally required to make get a new sticker.
"The Book / Brochure" just gives the number for a basic truck, what the maximum possibility is. It doesn't list how much each option reduces the number. For example, there is a model and package of F150 that has a payload over 3000lbs! Will you find it on a lot? Not likely. The sticker on the truck represents it as it sits.
It is surprising how low those numbers can sometimes be, and usually you see it on top of the line diesels. The diesel engine weighs A LOT more than the gas engine, so that is part of it, and all the components of the fancy packages weigh in as well. A gas engine XLT will have a lot more payload than a diesel Platinum. Good luck with your hunt!