Okay, now that you know about the weights, we can assign values to the different colored ones in order to make this easier to figure out.
Using this method, the orangish ball outside would weigh 11 units.
To make solving this puzzle easier, we'll assign the value of 1 to the brown weight, 4 to the crystal-like one, and 16 to the black. I picked these numbers because it's true that a crystal weight is four times heavier than a brown one; a black weight is four times heavier than a crystal one. So, a black weight is sixteen times heavier than a brown one (4 X 4 = 16). All this is how the weights earn their made-up but accurate values.
Thanks for your long explanation, but how's this going to help me?