Any weight you can shave off the total weight will help. This includes every part of the sail, including the type and amount of thread used in the stitching of the sail, the type of material used as the sail, the frame members, the hardware used to hold it all together, and the type of bridle (if any at all) used.
The frame only needs to be strong and stiff enough to withstand the most radical move you intend to make; anything more than that is "dead weight". This applies to all parts of the kite, indoor or outdoor. Most commercially made kites are built much stronger and heavier so they can withstand the abuse of less experienced flyers. No one likes a multi-hundred-dollar kite turning into splinters and torn material the first time they fly it.
Once you are familiar with the flight characteristics of a particular design, you can build it extremely light. Then you can fly with ease while most others are either struggling to fly, or totally grounded.