Cinemagraphs are still photos with elements repeated movements. They have recently gained in popularity, and rightfully so; a well done cinemagraph can be visually striking.
Cinemagraphscan be GIF or video files. Both can lead to larger files, when the film is high quality. GIF Graphic movie may be slightly larger than 3MB, you may instead consider streaming video.
You can see some wonderful examples of cinemagraph on Flixel; A hosting service for this type of picture or video. Take a look to see some of the great work people are doing.