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That 3500# max tow rating is an advertising dept stat. It assumes a LIGHTLY optioned Equinox, two 150# passengers and a full gas tank. PERIOD. This number must be reduced pound for pound by everything else that goes in the SUV. That includes optional equipment installed on the car.
The better number is the 1083# Payload you provided (THANK YOU) This is exactly what it says. No passengers are included, but it does account for all factory installed options. As Steve said, add up the weight of all expected passengers and SUV cargo, then add 10% - 12% of the desired camper GVWR. This is what the SUV is carrying and can not exceed 1083#.
As others have said, look at teardrops, R Pods and smaller pop ups. Keep the weights as described, then go enjoy the great outdoors!