Let's talk about aquarium light rocks, shall we?
Natural Slate Stone
These rocks are thin, and a good candidate if you want to build a fairy garden-themed or "enclosure" type of aquariums.
The whole package only weighs 5 pounds (2.2kg).
Ohko Dragon Stone
This may not be a "light" rock candidate, but you won't need more than 2-3 or Ohko dragon stone in a single aquarium.
Using the stone as the main highlight of the tank is an excellent idea. The same as the slate stone, the package only weighs 5 pounds.
Avatar-style floating rock
Not really a stone, but it's a cool one so I added to the list. Has the stone feature, and weighs just 3 ounces.