Most car trailers are 1700-2300lbs, they aren't light. Even the light ones are 900+lbs.
http://www.allprowest.com/3Open_CarHaulers.html Look at the 3rd row down. 6.6 feet x 14 feet AL frame open deck trailer, 910lbs. "Lightest Car Trailer on the Market," according to them. That's about as light as it's going to get, unless you use a dolly (250-400lbs?) and disconnect the drive shaft from the rear diff. Plan on 4000-4700lbs+ any extra stuff you want to bring.
And some extra mods like air bags will be a must, the Pilot we used had them added I'm pretty sure. Also a trans cooler.
I used to be very anti towing with a "poor" towing vehicle. I was very skeptical of the Pilot, it did way better than I was expecting. But definitely take vehicle weight into consideration.