Just as you might need more cowbell, you might need more tongue weight. Many have touched on this, but 10% of GVWR is the minimum tongue weight. 13% or so is recommended. 15% is the typical max tongue weight.
So, to illustrate, if your GVWR is 5000 pounds, you want a minimum of 500# tongue weight. "Ideal" 13% is 650# and max would be 750#.
Now the bad news. That's a whole lot of trailer to tow with a half-ton pickup.
GVWR of 9710# puts ideal tongue weight at 1263#.
Your RAM half-ton MIGHT have a payload capacity of 2000#. More likely, it's about 1750#. With ideal tongue weight plus roughly 70# of WDH, that comes to 1333#. Take roughly 1750# (estimated) payload capacity and subtract 1333#, and that leaves you with 417# of remaining capacity for humans, pets, and various cargo. Put differently, you are really pushing the limits of your tow vehicle's capacity. Note that the chart I shared includes "Gross Axle Weight Ratings" front and rear. All those numbers will come in handy at the CAT scales others have already mentioned.
Two other factors come into play. This trailer is over 36' long. That's one huge "sail" for crosswinds and semi-truck bow waves to push on. I can't overstate how much leverage an oncoming or overtaking semi can apply to that VERY long lever behind you. With oncoming semis (or wind gusts around underpasses in particular), the forces hit hard and fast. The oncoming semi first pushes the front of the rig toward the shoulder, but within a second, all that force is applied at the rear bumper of the RV. So this hard twist must be resisted, and the longer the distance between the RV's axles and the extreme ends of the RV, the more force can be applied.
Next, the tires commonly specified on a half-ton are on the "soft" side for ride...and this is particularly true for RAMs. They are known for ride quality, but that makes them softly sprung and their tires are biased toward ride comfort. I have a RAM, and when I tow my rig, I always increase the tire pressure in the rear tires to sidewall max. When unladen, my recommended tire pressure is 35 PSI. I run Michelins, and the tire is marked with a max pressure of 44 PSI. When towing, I increase the pressure to 44 PSI, and that takes out a bunch of spongy wallow and side to side wiggle as the RV applies loads plunging up and down and side to side. Sway is "side to side" and firming up the tires a bit resists that sway just a little bit more. Some will say that tire pressure specs are designed to handle the truck's full payload. Perhaps so, but when you hang 36' of wiggling RV behind the tow vehicle, stiffer tires help. And it's the rear axle that matters most, because that's where the big hinge is.
I won't repeat the guidance you've received about CAT scales. Only a couple of configurations of your RAM are set-up to handle your trailer. Hopefully you have one of those. But regardless, you are running near the edge, so your weights and balance (tongue weight) are critically important. Sure, add more tension to the WDH, but you're putting every bit of 10 pounds into that 10-pound bag, so you must be 100% aware of how much weight is where...and that you're not overloaded. Between the CAT scale, the PRECISE model of RAM you have, and that RAM weight chart, be sure you are dialed in as well as you can be.
And remember, Ford, Chevy, and RAM have really been in "towing wars" ever since Ford came out with the v-6 turbos that could tow 12,000#. (By comparison, my old RAM is only rated to tow 7700 pounds.) Like many such wars, expect exagerations and hyperbole - a.k.a. boasting. One specific configuration of the RAM claims it can tow 12,750#. Bear in mind that's on a perfectly sunny day, downhill, with the wind at your back, and no semis or crosswinds.
13% of that is 1658# of tongue weight. With the WDH thrown in, the remining payload capacity of the truck is less than 200#. They must have performed these tests with jockies doing the driving.
Did I exagerate? Yup, but perhaps less than RAM did with it's towing specs. You have serious work to do to dial in your RV and TV for the safest possible tow...even if you have the mondo model on that chart.
