If you are towing 9,000 pounds you will likely have at least 900 pounds of weight on the tongue. You have to subtract that from your payload capacity of 1,600 leaving you only 700 pounds for people and gear in the truck. Maybe less if your tongue weight is over 10%. If you're towing an RV it will likely be over 10%. If your towing a boat it might be less than that.
Trucks have a Gross Combination Weight Rating GCWR. This is the total weight the truck and trailer combined can weigh. That might figure in for your situation too.
Keep in mind there are lots and lots of different kinds of trailers out there: livestock, flatbed, dump, RV, boat, utility, cargo, etc. By far the hardest to tow is a hardsided RV. They have a huge frontal area of drag, huge side sail area, a high percentage of tongue weight, and very little ability to move weight around. A truck that might tow a 9,000 pound boat just fine might really be a struggling handful with a 7,000 pound RV.
