The graphic that bears the most weight, the gymnast if you will, at the center indicates a lot of what the association represents. It's top-heaviness keeps the flight and power of a gymnast from being tied down; however, its absolute symmetry balances it plausibly to the viewer's eye. The arcs imply movement and force without throwing the entire structure off kilter.
The font connotes ties to the Greek tradition of acrobatics and possibly even the Olympics themselves. It is light but well-proportioned and strong. The height compliments the width of each stroke--evenly spaced in all dimensions. By centering "USA" on top of "GYMNASTICS" in all capitals, the logo even construct a podium. The arcs of the graphic above hint at a final, victorious salute. High quality gymnastics--United States of America Gymnastics Association.
