I towed a little 4x4 trailer and just load it up. I think the thing doesn't weigh over 500 lbs, but its done it quite well.
I towed from SoCal to St. Louis and back with zero issues.
I also towed from Texas to Las Vegas without any issues AND I also towed from Las Vegas to Vancouver without any issues.
I would not hesitate to tow with it.

For my most recent move I'm moving about 4000 lbs of stuff, so the fit is being towed by a cheap old moving truck I bought. I spent something like 2k and 1500 fixing it. Super cheap to move from CA to FL.

 

The Honda Jazz is rated for towing in the UK and the Fit is the same car so I can't see any reason you can't tow something small, some have said that the Jazz has different shocks and springs than the Fit does, seems unlikely that Honda would manufacture 2 different rear suspensions for the same car but I don't know for sure. I think here in the US Americans like their big trucks and SUV's so we are kind of brainwashed into believing you need a full size vehicle to tow a dirt bike. I think as long as you use good common sense the Honda Fit is perfectly satisfactory for towing light loads. That being said I put my hitch on to use a cargo carrier

 

The European fits with the tow package have 4 wheel disc brakes not just disc fronts. FYI
The changes are discussed on pg3 of this thread

 

The pictures I've seen show the jazz a little bit fancier on the inside too, I saw one with climate control settings etc. Its likely marketed as more of a family car over there where as in the us its marketed as young persons commuter car. Honda would rather see a family buy a crv in the states so they steer you that way by keeping the fit more bare bones on the options and then telling you not to tow anything with it. If they sold the fit with a roof rack and tow hitch (like they do in the UK) they would probably sell a fair percentage less crv's than they do now, crv's cost more than fit's do so its in Hondas best interest to sell more of them, its in my wallets best interest to look beyond this

 

So this is a complicated subject, but to sum it up: European tow standards use much less tongue weight (around 5%) and a strict, low highway speed limit (around 50 MPH) while towing to ensure safety while the US uses a higher tongue weight (around 10%) and a higher towing speed limit.

Less tongue weight generally = instability/oscillation/trailer tail wag starts to happen at lower speed.


This is why essentially identical cars have a greater tow rating in Europe, or have one when that model has none in the US. Also note that small trailers in the US often don't have brakes, and that EU tow capacities usually require trailer brakes.

A guy on Jalopnik did a great writeup on this with more details. See here: Tow me down!

 

Interesting read, I wouldn't want to tow anything that heavy at 70 mph in a Honda Fit, I seen a guy flipped over off the side of I95 that was trying to tow a huge airstream travel trailer with a Chevy blazer. I guess where there is a lack of common sense the good old government has to legislate it for us.