Some other as important questions. What is the payload of the truck and what is the gross combined weight rating, and what is the gross vehicle weight rating. I have a 2013 Ram 3500 SRW diesel, and those numbers you quoted would be right on the line for me. My payload is 4,000 with a gcwr of 25,000 and a gvwr of 11,700.
At your trailers max weight of 16,000 you should have 3200 lbs pin weight, plus the hitch, plus gas, plus passengers,plus any other stuff in the truck, plus the weight of your truck. That weight should not exceed your gvwr. Assume your truck weighs 8000, you and mother weigh 300 (combined
), the dog weighs 40, the hitch weighs 200, and the pin is 3200, then you would need a truck with a gvwr of at least 11740 plus the weight of your fuel. So let's call it a gvwr of 12,000. If your trailer is maxed at 16000 minus the 3200 is a total axle weight of 12,800 plus the 12,000 for your truck, then you will need a truck with a gcwr of at least 24,000.
Clear as mud....
I'm not familiar with the new GM's but after all that crap above, I bet your ok.
2013 Ram Longhorn 3500 Crew Cab 6.7 Turbo Diesel, Aisin Transmission.
2014 Jayco Eagle Premier 351 RSTS, Mor/Ryde Suspension and Pin Box, 17.5" wheel upgrade, 18k Pull Rite hitch.