Well, if one has enough weight on the tongue of the trailer that it mashes down the back of the car, then one should probably redistribute the load so that it is less weight on the front. Otherwise the trailer will swing back and forth violently on the interstate.
Eh? Generally, the more forward loaded the trailer, the more stable it is. Unless you're overloading the tow vehicle. A trailer evenly balanced over the wheels is going to be a lot more prone to get into swaying on the interstate than one loaded forward, though I admit I don't know what happens when you severely overload the tongue. I've got a 15000lb receiver rated for up to 1500lb of tongue weight (with the balls to go with for big trailers), so it's not something I actually worry about... mostly, my concerns relate to matching my unloaded ball height with the other guys who tow so I don't have to crank the trailer up or down a lot to get it hooked up. Stuff around the property is light enough that it's not a big deal to toss a handyman jack on and lift it up if needed.
With those qualifications, I have a question: What would count as evidence that this is doable?
From my perspective, which is a blend of technical reasons but also "I want to be able to defend my decisions before a court," there is no such thing for a cross country move. If the car has no tow rating, towing with it is highly unadvised.
If you want to stand before a judge and try to explain how, in Europe, with totally different testing standards and license limits and road conditions, your car can tow XYZ, so you felt it was fine to do here, and that's totally unrelated to the accident, be my guest.
The testing standards are different.And, again, in this context, we're talking about a cross country move, which means interstates and mountains. Not just towing a trailer to the hardware store and back.
Could we show that the European and US Jazz/Fit have the same part numbers? Dig up and/or translate the owners manuals from countries with different norms? Could we make a video where the Fit stops a 1000# load from a certain speed at a certain distance? Does it help to reason that the Fit has 5 seats, and that having only 2 people plus a dog leaves about 500# of unused capacity that can count toward the trailer load? I ask because there's no need for the OP to do a bunch of research if opinions are "dug in".
And none of that matters with the different testing environments.
Well, my opinion is pretty well dug in, though I'll certainly admit that being a private pilot has something to do with that - the NTSB (accident investigation) pretty much lays into pilots if they're in a crash and are loaded outside the envelope. Unless it's a loading I'm quite familiar with (solo, two in the front, two in the front and kid in the back), I pull out the spreadsheets and do a weight & balance before flying.
But as for the unused capacity, I think you badly overestimate the load limits on small cars.
A 2015 Fit has a max payload capacity of around 850lb, minus fuel (so about 800lb usable). If you've got a pair of small adults in there, a light dog, and basically nothing else, you'd have 450-500lb left to work with, but that's not how people move. There's not going to be much left for the trailer tongue weight.
Look, you can be a test pilot if you want, and explain it to the judge. But it's a pretty stupid idea, and towing a U-Haul 5x8 trailer cross country behind a Fit, with a driver who has either never towed or only rarely towed, is a good way to the Darwin awards.