Focusing on a marine hydrokinetic energy application, this paper presents a combined geometric, structural, and control co-design framework for optimizing the performance of energy-harvesting kites subject to structural constraints. While energy-harvesting kites can offer more than an order of magnitude more power per unit of mass than traditional fixed turbines, they represent complex flying devices that demand robust, efficient flight controllers and are presented with significant structural loads that are larger with more efficient flight. While significant research has addressed the control problem, a much smaller body of research has addressed plant optimization, with no co-design effort to-date simultaneously addressing the geometry, structure, and control system. In this paper, the geometric and structural optimization is performed in what we term a nested sequential approach to minimize kite mass for a required power output, subject to structural limitations. The optimizer uses a control proxy function formulation to account for the closed-loop flight efficiency differences between different geometric designs, which accounts for plant-controller coupling without requiring explicit consideration of the controller within the geometric/structural tool itself. Medium-fidelity simulation results for a 100 kW ocean kite system illustrate the efficacy of the co-design process relative to a baseline design, and relative to a pure geometric/structural co-design that does not account for closed-loop flight efficiency through the control proxy formulation.