Yes, you need to weigh your MH and get, at a minimum, the front and rear axle weights. I have a 2006 National Seabreeze and have a 22,000/26,000 rating. My weight loaded (full water and load) is 18,980, so I'm 7,020 lbs under my max overall. However, my hitch is a class III hitch, but the manual/specs says I can only tow 5,000 lbs. My Acadia is 4,500 lbs so I'm good. As long as your loaded weight is 25,000 lbs or less you're good with what you have.
BTW - just because the class III hitch can be rated for 6,000 lbs (https://www.drawtite-hitches.com/learning_center/general-towing-classes) you should follow the manufacturers specs for your motorhome, as it's just not the hitch rating, but the hitch/frame combination.
Al