This article proposes the integration of structural sizing, topology, and aerodynamic optimization for a morphing variable span of tapered wing (MVSTW) with the aim to minimize its weight. In order to evaluate the feasibility of the morphing wing optimization, this work creates a numerical environment by incorporating simultaneous structural sizing and topology optimization based on its aerodynamic analysis. This novel approach is proposed for an MVSTW. A problem-specific optimization approach to determine the minimum weight structure of the wing components for its fixed and moving segments is firstly presented. The optimization was performed using the OptiStruct solver inside HyperMesh. This investigation seeks to minimize total structure compliance while maximizing stiffness in order to satisfy the structural integrity requirements of the MVSTW. The aerodynamic load distribution along the wingspan at full wingspan extension and maximum speed were considered in the optimization processes. The wing components were optimized for size and topology, and all of them were built from aluminum alloy 2024-T3. The optimization results show that weight savings of up to 51.2% and 55.7% were obtained for fixed and moving wing segments, respectively. Based on these results, the optimized variable-span morphing wing can perform certain flight missions perfectly without experiencing any mechanical failures.