The most critical thing, IMO, is not how much the rear drops, but how much the front raises. All of the steering and most of the braking is done by the front axle. Reducing the weight on the front axle reduces the friction force of the tires on the road with a corresponding decrease in steering and braking control. It has been reported on here that an F250 owner's manual said a WD hitch was required for trailers over 5000#. Search your manual for guidance.
There was recent coverage on here of a Ford advertisement that touted the weight carrying capacity of the F250 (I think) stating that a weight distribution hitch was not required. My opinion is that they were strictly talking about rear axle capacity and didn't consider the reduced load on the front axle that results from a heavy tongue weight.
The above is just my opinion, worth exactly what you paid for it. Several on here advocate towing on the ball on the heavy duty trucks, and some have reported good sway control from the electronic systems now being included with newer vehicles. I believe the true story is told by weighing the vehicle and following the manufacturer's recommendations.
Al
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“You cannot reason someone out of a position they have not been reasoned into"
Al, K5TAN and Missy, N4RGO WBCCI 1322
2002 Classic 30 Slideout -S/OS #004
2013 Dodge 2500 Laramie 4x4 Megacab Cummins
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