As I mentioned in a related post, figure the pin weight of a BH3670 to be at least 2950 lbs. and the tow weight to be 14500 lbs. That's with a full compliment of summer clothing, bedding, and necessary "stuff," along with a washer/dryer in the closet. Increase that if you have water/sewage in the tanks, a generator, the wife's combat boots, or Grandma's heirloom set of cast iron cookware inside.
From the spec. sheets, older GM2500 pickups were close to their limits on this. The newer (2010 or newer) ones have higher ratings that rival the older 3500 ratings.