Thanks for the replies so far. I'll try to fill in the missing info.
The sticker inside my truck door says "Combined weight of occupants and cargo should never exceed 1638#". My truck is a 2014 Silverado 1500 Crew Cab, 2WD, standard bed, with 5.3L V8 and 3.42 gear ratio. The truck owners manual states a 9700# tow capacity for this setup. The truck is equipped with tow package and factory brake controller. The underside of the receiver tube on the truck states a 1200# max tongue weight.
The specs for the possible new camper says UVW 6935#, GVWR 9500#, and dry hitch weight 855#.
My current camper sticker says UVW 5326# and GVWR 7500#. It doesn't give the dry hitch weight, but 12% of the UVW would be 640#.
Typical trips are me, my wife, and 2 kids with bicycles, firewood, cooler, etc. in bed of truck. Tanks in the camper are always empty. Please let me know if I've left anything out.