Like others I'm guessing you're too light in the tongue. Yes I agree that getting it weighed (try a cat scales, a local moving company, the city landfill) Barring getting it weighed you could make a few tests.
You mentioned your water tank is behind the axles and the gray and black tanks are in front of the axles. Try draining the fresh and use a hose to fill the gray and black and take it for a drive.
Or go to home depot and buy about 200 lbs of the bagged playground sand and put the bags on a tarp as far forward as they can go in the trailer. Pull the generator off and go for a test drive.
Maybe you can find a way to use some ratchet straps to temporarily mount the generator to the tongue long enough to go for a test drive. If the rear rack is removable make sure to remove it also for the test.
If it tows fine after that then you just have to figure out how to load to keep the an adequate tongue weight.
If and when you do take the trailer to the dealer make sure it's on a day they can look at it. Have the fresh tank full, the generator on the back, and and install instructions for the hitch downloaded and printed out.
Good luck with it, it doesn't sound like an enjoyable tow as it is.