I don't understand your problem. The factory's empty weight was no doubt what the truck weighed on their scale at a certain time, temperature and humidity with a few gallons of fuel and nothing else. After the fuel tank was filled you weighed it, with you in it, and saw a very unlikely even number of 6200 pounds. Both front and rear weights were even numbers, perhaps rounded off to the nearest 10 or 20 pounds. Both scales have a plus or minus tolerance of a certain percentage, either or both may be out of calibration and the one you used seems to provide a reading to some closest even number. You and any added fuel after it left the factory and those variables could certainly account for that 172 pound difference.
GVWR is not a legal requirement, it's a recommended number to remain within to ensure a wide safety envelope for varying driving conditions. Your never exceed weight number would be the sticker's rear axle rating minus your 2680 rear scale reading.
