Although we don't use differing tires on our Fit we've been doing it routinely for 25 years on racers and A/X'ers to improve lap times.. And it has always worked.

There are 2 major things to bear in mind:
1. The front tires should be one size larger (depending on HP) than stock and slightly smaller in diameter so the greater weight of the tire is at a slightly smaller radius to keep the torque required to turn the tire about the same as stock and therefore doesn't eat any power.
2. The rear tire diameter should be slightly larger than the front tire and one size less cross section than stock, again depending on HP and weight distribution to prevent the hobby-horsing that occurs on FWD when the rear wheels are smaller than the front.
Lighter wheels are beneficial of course but not part of these considerations.

Here's an example we did recently:
A FWD car with 225/45x17 tires (24.97") improves lap times by substituting 235/40x17 (24.40") fronts and 215/45x17's (24.61") at the rear. Lap times improved by 5%. Another is on the way.

An example of this can be seen on you tube's 'hyundai sundae..". The Azera in the video is equipped with Pirelli M+S 245/45x17 front and 225/50x17 rears. The Azera is a family crusier unprepared in any performance upgrades except lowered front springs and performance rear shocks. Handling on a street vehicle doesn't get much better than that.

PS we have never found any benefit from mounting wider rear tires on an FWD vehicle. Neither have performance manufacturers; the wider tires are always on the driving wheels.
PPS as long as the tires are close to same diameter and the wheels are the same dia there is no difference in appearance. Can't tell unless you actually measure them.
good luck.

 

The 205/50x15 and 195/50x15's are a good choice.

 

Very easy and doesn't cost a dime. Just disconnect the front antisway bar and tether out of the way. A Fit has soooo much understeer its ridiculous and without the ASB its pretty good handling car.
Or you could add a rear ASB but that dorsn't help track manners gets too tipsy.

 

Run the wheels that fit the approved rim width range for the size tire you are running. Wider wheels at the rear may or may not help, depending on your tire pressures. Having a little higher pressure rear helps decrease understeer, as Honda mentions doing on the 09's, not once but twice.
But more traction at the front is mandatory.