You say you are towing a trailer that weighs about 13,000 lbs. You didn't say what type of trailer - travel trailer?, a loaded equipment trailer? etc.
The tongue weight of the trailer should be about 10-15% of the trailer weight, which would be approximately 1300 lbs to 1950 lbs of tongue weight in your situation. This tongue weight could unweight the truck steering axle enough to cause the combination of truck and trailer to handle poorly (especially in curves on a downgrade). A properly set up weight distribution hitch would work well in this case.
Whether or not you use a weight distribution hitch, it is very important to know the actual weight of the truck and trailer separately, and to know the actual tongue weight of the trailer. One method is to load everything as if the truck and trailer were ready for the trip. Then, take the truck and attached trailer to a scale. Place the truck with both axles on the scale and record the weight of the truck. Next, disconnect the trailer (ensuring the jack is not on the scale) and record the new weight of the truck. Note and record the difference - this is your tongue weight. Finally, reattach the trailer to the hitch and weigh and record the trailer axles only.
A tonnage gauge (like the one shown in the photo) is a useful tool for measuring exact tongue weight.
- John
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