My wife needs a wheelchair from time to time and it takes up a lot, almost all the space in the Fiat. I want to put on a hitch mounted rack on the back but I need a way to keep it fairly clean. Is there some kind of bag I can put it in to keep it fairly clean and dry?
Samples:
http://www.topmobility.com/wheelchair-covers-s629.htm
Any sort of bag that isn't really expensive (like Thule sells) is going to either be in tatters or leak I think and it's going to flap around a lot. Maybe you could take a big sheet of cordura to a sail shop and have them stitch you something with velcro or eyelets for bungies in the right places to seal up around the chair?
It wouldn't be too hard to fab up a box from scratch if you have access to a brake that do 3/16" aluminum diamond plate and a TIG. Add piano hinge and lock loop... bonus that it's harder to steal.
May be a bit cumbersome on a Fiat 500.
http://www.discountramps.com/aerfoil-scooter-carrier-cover/p/SC-COVER-BK/

Can you just tow it like a car behind a motorhome? I mean, it doesn't solve your problem. But I want to see a picture of the Fiat set up like this. Obviously I am of no other assistance.

You might be able to find someone who makes custom car covers locally that could do it inexpensively.
the M-I-L uses a wheel chair and they bought a light weight one for traveling as they don't always need the big one.
could she use this and squeeze it into your car?

A bag cover likely won't help with filth, much of that gets blown up from below, and the bag is open to the bottom. Bags are also a royal pain to deal with folding and unfolding, especially when they are wet and muddy.
The likes of a flat bottom carrier and clam-top lid are much quicker to work with and do a far better job of protecting the wheelchair from dirt and wetness.
In reply to Datsun310Guy:
We tried on of those too but it didn't save that much room. The problem is more with the car being comically small than the chair being too big. I was trying to avoid something heavy like a box for the same reason but I may look at one of them if I can get a light one.
They're ugly as sin and dog slow, but there are also roof top carriers for wheelchairs. Things like this:

These folk have an interesting looking zipper bag that fully encases the wheelchair. http://www.wheelchaircarrier.com/#!accessories/cgfa
