The trailer pin/GN weight can be from directly over the trucks rear axle to 4" inches forward of the rear axle. There can be little to no weight transferred forward to the trucks front axle. Weight transfer has much to do with a trucks wheelbase/pin location and actual hitch weight.
My short bed truck pin is zero over the axles for zero front axle gain or loss.
My old one ton DRW long bed chevy has its pin/GN hitch weight 3 inches forward of the rear axle with a 60 lb gain on a 16000 ln GN stock trailer with 4800 lb hitch weight.
Now lets look at some actual numbers from GM weights calculator Model Information - Online Ordering Guide
that figures all std and options for you. We have no idea of all your trucks options and std packages but I configured a '13 3500 DRW loaded LTZ 2wd extended cab long bed truck through the weight calculator.
It shows the LTZ DRW has a 5900 lb payload per GVWR.
It also shows a 6600 lb payload on the trucks 9375 RAWR.
GM specs also show a 16500 lb for a bumper pull.
Gm specs also shows a 22800 lb tow rating for a GN/5th wheel trailer.
Isn't it amazing how much we can tow and carry now with the new gen trucks. And especially GM weight calculator that eliminates the old theory that tow ratings are from a stripper model. Of course most folks have know that for many years now.
I weigh all my vehicle on a single platform scales at my small town local feed mile/grain elevator for free (scales are open 24/7). Simply drive the fronts all the way on for the front axle. Now pull forward for front and rear axle weight. Now pull forward till the front axles are off the scale . Now you have the rear axle weights.
IMO everyone should know there truck separate front and rear axle weights with and without the trailer.
EDIT; Hmmm, just saw your new post. Your truck doesn't have a Cummins unless it a RAM. And does your truck have 4 rear tires or two rear tires.