Hi RonS, welcome to the board. Good for you, wanting to build your own teardrop trailer, or perhaps convert a cargo trailer to your liking. I built a 4x8 woody that weighs in at about 550 lbs, loaded with all of the camping gear. I also have a 40 inch wide 6 footer, and it only weighs 245 lbs, empty. So, to answer your question, Yes, it is totally possible to construct one of these little jewels that is well under 1000 lbs.
I have noticed that most of the heavy-weights, construct their rigs out of heavy 3/4 inch plywood, have massive cabinetry and probably a heavy-duty frame to boot. Adding bells and whistles, such as leveling jacks, storage boxes, car wheels and tires, also increases the final weight.
The sides of mine are 1/4 inch plywood, and it is as solid as a rock. Hey, they build airplanes out of 1/8 inch plywood. Good luck on your build, which ever way you go. Remember, ask questions, take pictures and post 'em, we love pics. Now, get busy, buy that trailer frame and start bolting things together.

Roly