There is no difference in weight between the Mid-grade and the UltraEdge. The only difference is that the standard blades (both Mid and Heavy grades) are made with a clear polymer and the UltraEdge blades are made with a translucent white polymer. The UE is called that because it better produces blade color all the way to the "edge" of the blade tube where it meets the tip. Emory likes to use the standard blades in the demo videos. They have a distinct silver color.
So to answer your question on weights...
The Mid-grades (standard & UltraEdge) are very lightweight. I don't think you'll be able to find a better simulation of a "weightless" blade that you can actually fight with.
The Heavy grades (standard & UE) are about 2-3 times thicker than the mids, and naturally are 2-3 times heavier. This weight increase will seriously affect how the saber handles as well as how much punishment it can take. Unlike the mids, the heavies can take an astonishing beating and keep going.
I hope this answers your question.
An excellent summary, well deserving of a point IMHO.