If you want the backdrop to look darker, put less light on it, or move it farther away from your subject light boxes (e.g., with family on right, you'd use a 30ft to give a floor piece and still have room to move the group to foreground).
In turn, more light on the backdrop will make it appear lighter (subject lights will spill to backdrop). One great way to get variety is to use spot lights (e.g., from floor, from side) in parts of the backdrop and leave other areas in dark. There's a very fancy term for it: "chiaroscuro" (distribution of light and dark areas, esp. paintings). Also, you can use gels to shift color cast.
Dance Studio Backdrops: It's a tough call but sometimes you have to take into account the stage lighting -- if the stage lights are strong, your backdrop selection should take this into account -- if we go too light on the colors, the stage lights will over-light and wash out the colors.
