Hi Eddie,
Congratulations on your new rig and welcome to the Heartland Owners Forum.
The Bighorn 3160 has a GVWR of 15,500, and although the empty pin weight is shown as 2,095, you should plan on an actual loaded pin weight of around 20% of the GVWR, which would put you closer to 3,100. Add to that the weight of your hitch, bed liner, bed cover, tools and cargo carried in the truck, pets and passengers and you could have a payload of close to 4,000 lbs. That would put you into a late model F350 or GMC/Dodge 3500.
To get a more precise answer, let me suggest you visit
Fifth Wheel Safe Towing, a website developed by another Heartland owner.
And let me also suggest that whatever truck you look at, before buying, find out the actual payload and fifth wheel towing spec on that exact model/configuration.