To repeat with BillyW said you have artificially low payload on that sticker. To meet the GVWR of 10k your payload is calculated as the difference between the 10k and your truck weight. The 10k limit is for registration related issues and is not a reflection of the capability of the truck.
For 2016 the 2500 is the same as a 3500 with the exception of the rear suspension and maybe wheels depending on what package you selected. Expect the same is true for your 2013 (would defer to a Ram owner to confirm this shortly).
Buddy of mine has a 2012 Chevy 2500 and had a payload of under 2k. He put on different wheels and tires, added Timbrens and hauls in excess of 3k in his bed comfortably.
Take a look at this thread
Improving Ram 2500 PayloadGood luck,
Stu
