Why is a weight and balance graph lozenge-shaped? I have tried to find the answer but it seems to be really hard to find. Why is it not a square?
In a strict mathematical sense the graph should be a extended to a complete right triangle, not a rectangle. However there are practical limits on how far forward you can fill the compartments so the graph can be cut off at 83 inches in this case. and the top is clipped because increasing weight above that point reduces performance below design intent and angers bureaucrats.
The reason for a right triangle is because the acceptable location of the center of mass is more critical at increased gross weight. When the plane is very low weight the center of mass can be very far forward and not overwhelm the tail down force and leverage. At high gross weights the tail needs more leverage to counter the nose down moment, so the forward limit of the center of mass must be brought back closer to the center of lift. There is no angle on the aft limit side of the chart because moving the center of mass behind the center of lift, at any loading, will make stall and spin recovery impractical to impossible on a traditional wing and tail layout.
The slight radial flair in the particular chart pictured is simply styling.