First, are you sure you don't already have load rage D tires? Because, at roughly 1760 pound load capacity per tire, a load range C seems hopelessly inadequate. https://www.etrailer.com/Trailer-Tir...AaAvTmEALw_wcB
If you had load range C tires on that nearly 9000 pound rig, count your lucky stars that they didn't do the China Bomb thing.
Assuming you might mean switch from load range D to load range E....I'll elaborate on that move.
Whether to move to load range E from load range D is really a matter of math. Does the GVWR of your rig crowd the upper limits of your stock tires? If so, it's a good idea to move up and buy some extra safety margin. On the other hand, if the factory tires actually offered up a substantial margin of safety, buying a quality tire (e.g. Goodyear or Maxxis) is more than enough while sticking with a load range C.
Rockwood...SHAME ON ROCKWOOD...does not publish GVWR. They do publish dry weight and CCC, or "cargo weight." Add them up; it's not hard. But to FAIL to publish a simple, and CRUCIALLY IMPORTANT, number, the GWVR, is unconscionable. Using a 2020 to illustrate - your GVWR is 8782 pounds. Let's be reasonable and add a bit of margin for unintended overloading....let's call it 9000 pounds. Should you overload? Of course not. But unless you're on a friends and family discount basis with a close and convenient truck scale, you won't know from trip to trip. And as time goes on through a season, more and more junk accumulates in your rig. Anyway, I digress. Stick with 8782 if you're fastidious...you'll soon see it doesn't matter.
According to Goodyear, load-range D tires are able to carry 2040 pounds each. X 4 that equals 8160 pounds on the tires. That's a real number...not some estimate. The same 2020 spec says that the dry hitch weight is 782 pounds. Let's make that 800 pounds with, say, two x 6 volt golf cart batteries and full tanks of propane. You get to add the tongue weight to the tires' capacity, because that much of the 8772 pounds is on the tongue, not the tires/axles.
A little math reveals that load range D tires might be left carrying 8000 pounds or more.
That's obviously cutting it mighty thin, and if you overload the rig even a little, you've exceeded the tires' rated load capacity. As others have suggested, many RV manufacturers use the "barely enough" method of selecting tires. Frankly, an 8782 pound GVWR deserves 15" tires and considerably more margin for error. (larger wheels/tires carry more weight with the same load range tires...and wider tires carry more weight. 205 75 14 tires are very small for a rig the size of yours.) Check your wheel width, and you may find that a 215 width tire will fit your rim width just fine and carry more weight...because there's more air volume inside the tire.
So, load range E it is...if you can find them in 14's. You will pickup roughly 100 pounds per tire in load capacity...in other words 400 pounds of margin of safety. These tires will be slightly "stiffer", but if you use Goodyear's load charts, you may
be able to reduce tire pressures slightly to soften the ride while still maintaining a margin of safety. https://www.goodyearrvtires.com/pdfs/rv_inflation.pdf
At 65 PSI, the E's will out=carry the D's, but if you use the pressure/load charts Goodyear offers, you may be able to get away with 60 PSI and still have the right load carrying capacity. Use the charts with the tires you choose.
This doesn't apply to you, but it's also fair to point out that you can overdo this process. If you swap D's for F's, your rig will ride like a Flintsone car riding on rocks. There is a Goldilocks point at which the tires match the load with a reasonable safety margin, and the ride is reasonable enough to avoid shaking your rig apart. Of course, you won't find 205 75 14's in load range F, because it just makes sense to go with a bigger tire and wheel combo to get the load carrying capacity.
Assuming you actually had load range D tires, the load range D tires were "legal," but barely enough in your application. If you had load range C tires on that rig, you got very lucky to not have a massive blowout and rip out your fender wells. Nuff said.