What SUV's will tow Jayco Jay Flight 32TSBH or Eagle 324BTS

The hitch weight on either of those Jayco trailers is going to be much higher. I have a 2011 32BHDS and my tongue weight was 1,280lbs with a Reese Dual Cam hitch (total trailer weight of 9,600lbs loaded). I have a ProPride now and I'm probably closer to 1,400lbs. 815lbs is EXTREMELY light for a 10,000lb trailer, probably to the point of severe sway when going down the road.