I had a lot of trouble with this too. Two horse trailers that are still in safe working order were hard to find in my area. The dealerships nearby would post one online, but by the time I'd call it had "sold" (not sure on this, maybe they wanted me to have to buy a new trailer? ). Anything local I found in my price range was covered in rust. I ended up buying an older all aluminum trailer. It's an '01 4-star that I paid ~$7k for, which was more than we wanted to spend, but at this point I'd been looking for a trailer for and entire year. It is a good quality trailer though, and it tows much better than I remember the old steel trailers my parents always had. It's also got a bunch of nicer features not on newer, less expensive makes.
If your tow vehicle can only pull 1 ton, I'm not sure you'll have an easy time finding a trailer in that weight range without a horse, though. My all aluminum trailer weighs between 2500-3000 lbs empty, and the horses weigh 2000 lbs or so, plus weight of any equipment, feed, and water I load. You might consider purchasing an older truck that will have appropriate wheel base and towing capacity. Under-powered vehicles aren't any fun on the highway hauling live weight. Even though my Land Rover Discovery weighs more than the trailer and has a towing capacity of 5500 lbs (more than my loaded weight with one horse), I go up hill at about 35 mph here in the Ozarks (we have some crazy steep terrain here). I have trouble keeping the rig stable at more than 55 mph on the flat. It chugs along at low speeds and I can't complain for the price I paid for (free), but I absolutely can't imagine trying to tow this trailer loaded with an even smaller truck. I'm not sure it would even move! Stopping can also be a concern if your trailer seriously outweighs the tow vehicle. In fact this affects all the dynamics when towing and can make the trailer fishtail and shimmy and whip your vehicle around while it does it. Like I said, I've got this problem a little myself, and on paper, my truck IS big enough.
If you're determined, try to find a no-frills all aluminum without the dressing room or extra height. I believe some trailers also have some composite components specifically to be low weight, so if you can find one, that would be good. That should cut the weight down some, so if you load it minimally you might be close to your tow capacity. This should be ok for short hauls at low speeds. For the price of the aluminum trailer, though, you might be able to get a steel trailer like a Calico and an older more appropriate truck.
Tug on anything at all and you'll find it connected to everything else in the universe.~John Muir