Ok, so a couple of things and sorry but I don’t think you will like the news.
Whenever you are figuring weights you should use the loaded weights not the empty or dry weights.
The max tow number they give you is a marketing ploy. In reality you take your trucks GVWR and subtract that from the gross combined weight rating GCWR.
I looked up the GCWR for your truck, it is 12,800 lbs. Your GVWR is 7100 lbs.
https://www.chevrolet.com/content/da...ring-guide.pdf
12800-7100= 5700lbs. This is the most you can expect to tow.
The trailer you are looking at is 6500 lbs, it is too heavy for your truck.
You also cannot exceed your payload rating. The hitch weight is included in the payload. You need to use the loaded trailer number to find the actual hitch weight.
6500 lbs trailer when loaded x .12= 780lbs. (12% of the loaded trailer weight)
The hitch weight plus all of the occupants and cargo can’t exceed the payload capacity which is found on a sticker inside the drivers door. Make sure to use the number on the sticker for your truck not a generic number from a website.
I know this is probably not what you wanted to hear but I think you need a smaller trailer or a bigger truck.