Now that you have those numbers, you can look at your axle weight ratings, looks like your front is 6k and your rear is 7k from the picture you posted earlier.
That means you've got about 900 lbs you can add to the front axle, and 3600 lbs you can add to the rear axle. Looks like your weight as measured is about 600 lbs heavier than what it supposedly was when it was built, that would be anything you've added to the truck already (hitch, any people besides the driver, etc).
You're about in the normal ballpark, because most of the weight of the pin is going to be centered directly over your rear axle and it is going to see 99% of the weight.
That means your truck is rated to handle, presuming you weighed the truck with the hitch in the bed, a pin weight of about 3600 lbs as it was weighed. If you add people or gear to the truck, these numbers are going to change, but suffice to say you're rated to handle all but the very biggest of toy haulers/rvs out there. The Valor you are looking at SHOULD be no issue for your truck, provided your truck was weighed relatively similarly loaded to what it will be when you're hauling the camper. If your hitch wasn't in the truck, be aware that you need to reduce your allowable pin weight by the weight of the hitch.
When it comes to RVs and pulling them, the numbers you REALLY need to watch are your axle ratings and the GROSS pin/hitch weight of the trailer. Payload should be watched, but I personally argue that the axle ratings are more important. The 'max tow rating' is based on a series of tests involving getting up to a certain speed within a certain amount of time/distance, stopping within a certain amount of time/distance, and several other factors (and I don't even know what all of the criteria is), and for the most part it's just for bragging rights.
As for GVWR and GCVWR, these are the max numbers your truck and truck/trailer combo are allowed to weigh if you're using them for business/to make money (they aren't typically enforced by law enforcement for RVs BUT with how lawyers and insurance companies are these days it's a good idea to follow them, there is risk of liability if they're exceeded and something happens. It's a relatively low risk, but it is still a risk that an ambitious lawyer could latch on to).