Hi Bowman,
Congratulations on your new Cyclone and welcome to the Heartland Owners Forum.
There are two loads you have to be concerned with: 5th wheel towing capacity which is horizontal load, and payload which is vertical load.
Your 3800 has a GVWR of 18,000 lbs. The empty/dry weight spec is probably not anywhere close to the actual weight, which could easily be closer to 16,000 lbs because of options. There should be a sticker on the entry door frame showing the actual empty/dry weight as it left the factory.
As you put your stuff in, and add a little water to the tanks, it's pretty easy to add another 1000 lbs. So you could get closer to 17,000 lbs even if you think you're traveling light. The only way to know for sure is to go to a scale and weigh the rig.
Your F250 probably has a 5th wheel tow capacity of around 16,000 lbs. So depending on how heavy your rig really is, you could be overloaded on the horizontal load. This will be especially obvious on hills; both up and down. Sometimes going downhill can be a much more serious problem than going up.
You probably have a payload capacity around 2,600 lbs. That covers the pin weight, the weight of the hitch, bed liner, bed cover, tools, passengers, pets and anything else in the truck. The hitch weight spec of 3,100 is not likely to be close to actual. You could easily be over 3,500, especially if "we don't pack too heavy" means no toys in the back. The end result is you could be seriously overloaded on the rear axle of the truck, to the point of unbalancing the truck.
Most people recommend a 1 ton dually for a trailer of this size.
You can find more detailed information at
Fifth Wheel Safe Towing, a website created by another Heartland owner.