Vehicle
ipacman, it is good you are verifying the weights for your tow vehicle. However, you may be slightly confused on what these weights mean.
The GVWR of the truck is the maximum weight the truck can be, loaded with gas, all passangers, all installed options and all cargo. The GVWR of the trailer is the maximum weight the trailer can be, loaded with water, propane, food, clothing, personal effects and any sewage.
The trailer will have a 'dry weight', which is the weight from the factory. Don't rely on this, because it often does not include all accessories installed (by the dealer). However, it does provide some indication how much weight you can carry in the trailer. Hitch weight is the maximum weight the HITCH can stand and has nothing to do with the capabilities of the truck.
GAWR is the maximum weight applied to the rear axel of the truck. And GCWR is the maximum weight of the truck and the trailer. One final piece of information and you are ready to start computing. Any trailer adds some weight to the truck. For a fifth wheel, this is called 'pin weight' and is generally 10 - 20% of the trailer weight. I don't know what it is called for a travel trailer, but I think it is generally under 500 pounds.
So, you need to get an idea what the weight of your truck is, loaded with people and gear for travel, and the weight on the rear axel. The best way to do this is on a scale. You may be able to estimate it, but in this case be sure to leave plenty of room for error. As long as the values you get are less than the GVRW and the rear GAWR respectively, you can continue (if not, you have to lose passengers and/or gear, or all go on crash diets
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Now, subtract the actual weight of your truck from the GCWR. This will tell you the maximum weight of trailer you can tow. If this amount is over 3500, you will have to cut it down to below the hitch limit or get a higher rated hitch.
One final step. Find out how much weight (downward force) the trailer adds to the truck, and make sure this does not cause you to exceed either the GVWR or GAWR of the truck, and you will be within specifications.
Note that although you may be 'legal' below the maximum specifications, you may not be comfortable right at the limit. Many people allow themself 20% or so as a buffer.