Grand Design says your 375RE is a 13,600 lb. unit (dry weight) and that it has a 3,000 lb. kinpin dry weight. In with your documents, you should have received a sheet from Grand Design's certified scale showing the actual weight, kingpin weight--right and left.
If your trailer's anything like my Reflection trailer, your actual weight is probably somewhat over 14,000 lbs. and the kinpin weight might be pushing over 3,500 lbs. And that's before you've loaded your "stuff" into the trailer. My kitchen side of the trailer weighed 700 lbs. more than the entrance side--surprising.
The only way you can be assured of your truck meeting the specs is to go put your trailer and truck on a certified scale--and then weigh the truck only including fuel and any "stuff" in the truck.
Sure your 3/4 ton diesel truck will tow it. But how would it handle in an emergency maneuver or in a heavy braking situation? That's when the dual rear wheels come into their own. And what many RVers don't realize is that duals are just not that more expensive than SRW 3/4 ton trucks.
Sure most dealers and your salesman are going to tell you your truck will handle the load. They only lie when they're moving their lips--their general nature. What's funny is that my dealer wasn't about to hook up my Reflection trailer to any truck that wasn't equipped to handle it.
My 2003 F250 7.3 (60 hp tow tune) diesel was in too good of condition to trade in for a newer, heavier truck, so I purchased my Reflection 323BHS to match my truck. I have the heaviest suspension available that year with the helper springs and I added a set of AirBag 5000's and a TruCool tranny cooler. My trailer is just over 11K, and my kingpin weight is just over 2K lbs. That's under the posted max fifth wheel towing weight of 13,200 and 2,500 kingpin weight. As with any 3/4 ton truck, the kingpin weight is the problem (more than the total weight.) Max out my weight carrying and I'm far above the kingpin/bed weight capability.
And we're not suffering in any way in our Reflection bunk house trailer. It suits us perfectly. as does our truck.