Advice needed with wheel size and gear ratios.

Larger diameter tires will essentially reduce the gear ratio numerically. You will lose some pulling power.

I personally wouldn't see any benefit in the change but some obviously do. They sell lots of aftermarket tires and wheels.

Make sure whatever you buy has a load range equal to or higher than original.

Larger circumference tires raises the gear ratio which reduces towing power.

By going from 265/70/17 (31.8") to 35" tires you're are essentially reducing your rear axle ratio by 10%. From 3.73 to 3.38.
Looking at Rams towing chart going with a 3.73 tow rating of 10,350 to 4.10's increases it to 13,350. Assuming that reducing 3.73's by 10% your new tow rating would be 7,350lbs. If you tow less than that then all will be good.
JMO but I can't imagine a 2500 5.7 with 3.38 gears. Your mpg would take a big hit and towing power would be sluggish.
Remember too that your 1500 weighed considerably less than a 2500. And you already started out better with 3.92's over 3.73's.
If you had 4.10's in the 2500 it would be better.

Your existing tires are apx 31.6 inches tall, so the 35" tires will make a very noticeable diff in towing performance.

Jerry

In addition to affecting towing performance, the taller tires will negatively affect braking performance as well. The taller tire is a bigger "lever" acting upon the braking surface of the disk/drums. Taller sidewalls are also going to have more flex so you may experience more swaying as you pull. While taller tires can make a truck look better and do make it perform better off road they otherwise hinder a truck's performance.

Don't forget that when you raise the truck, you'll now need a longer drop on your hitch which places more strain on the receiver hitch.

The other thing not mentioned outside the reduced pulling power and breaking power is fuel economy. Your mileage will decrease 2%-5% for every inch added in diameter. If memory serves my brother lost about 3 mpg when he put 35s on his 2500 with 3.73s.

Edit: Double post - sorry.

Not only do you decrease effecive wheel torque by the %5 size difference, larger tires weigh more. 10 pounds or additional rotational weight per wheel has a far more effect than 40 pounds in the cab or bed. As noted by PMcColley, this affects acceleration, braking, handling and fuel consumption all negatively.

Don't do it. People who put bigger tires and aftermarket exhausts do not tow RVs. The engine load is far too high. What is acceptable as a compromise lightly loaded becomes obnoxious when towing a high walled RV.

I would keep an eye on your transmission temps too. Big tires and towing = short transmission life.

It is a safe bet that if changing tire size provided any advantage (especially increased fuel efficiency or pulling power) the manufacturers would have implemented them and bragged on their performance.

Style has little relationship to performance. However, it can make us happy