The cabins of most 13 ft and 14 ft trailers are 10 ft. The rest is frame and tongue. RV standards say that the entire length is what determines the length of the trailer. So, I'm not aware of a manufacturer past or present of a a 10 ftr. The newer the trailer the heavier it will be. You might find a vintage 70's Boler
in the under 1000 pound category. It won't be under by much. Most 13 fters weigh between 1,100 and 1,500 pounds.
I think you are looking at a popup - motorcycle sized, or a teardrop. The Aliner is the only hard sided motorcycle popup that I know of.