It is a tech issue. Overseas, Jazz gets different springs and shocks. Americans don't like hard riding cars no matter how small. We get squishy sprins and shocks. Have you carried a couple of 200 pounder passengers? Its not fun.
Thats why if you are going to tow much with a Fit you need the Monroe AirLifts.
I towed my lawn tractor on the little TS trailer with and without the rear Airlifts. Towing 900 lb ( 408 kg) with the stock Fit was uneasy. No problem with the AirLifts. we didn't measure the tongue load but guess about 150 lb.

 

It's been said before. Payload capacity according to the Honda specs is about 1000 lbs. 150 lb. tongue weight is nothing from a suspension standpoint.

Any car that is towing a significant fraction of its capacity will handle quite differently: I'm not sure why you would expect otherwise. I think people are spoiled from towing things with their giant pickups and SUVs these last 10 years or so. 20-30 years ago, a 3000 lb. car was a pretty big tow vehicle and 4000 was the weight of the biggest GM sedans. Now, 4000 lbs. is a typical mid-sized car. Suspensions are also much stiffer now: spring rates and damping, than they were 20-30 years ago.

 

I left my new trailer on the fit loaded with my dirtbike. Average MPG on that tank was 32mpg.
Bike Dry weight is 262lbs
Trailer Weightis 120lbs

Estimated load 500lbs +or-

You COULD see a slight drop in the rear of the car, but nothing really note worthy.
Tongue weight I didnt measure, but it well under 100 lbs. If you are near your 150lb limit, I agree better shocks and springs would be best if you were going medium to longer distances. Short rides, I still wouldnt bother.

 

Here it is FINISHED and painted to Match the Vivid Blue!