Morphing wings, a pivotal technology for next-generation aircraft, enhance aerodynamic performance by continuously adapting their shape during flight. However, most existing topology optimization designs primarily focus on achieving target airfoil shape, while the load-bearing and actuation performances are rarely considered in a coordinated manner, often resulting in insufficient aerodynamic load capacity or excessive actuation demand. This limitation arises from the fact that morphing, load-bearing, and actuation performances together constitute a highly nonlinear and strongly coupled multi-objective optimization problem, which poses significant challenges to conventional optimization methods. To address this issue, we propose an adaptive volume-regulated nested topology optimization framework to achieve the collaborative design of morphing, load-bearing and actuation capability for morphing wings. The original highly coupled multi-objective optimization problem is decomposed into two hierarchical levels: the outer level focuses on optimizing the target aerodynamic airfoil, while the inner loop regulates the actuation and load-bearing performance. This decomposition effectively eliminates gradient conflicts and reducing the overall optimization complexity. Furthermore, an adaptive volume strategy is introduced to bridge the inner and outer optimization levels, in which the structural volume is dynamically adjusted according to the convergence state of the inner-level optimization, thereby enabling efficient material utilization. The effectiveness of the proposed framework is validated through a series of morphing wing trailing-edge examples. Numerical simulations and experimental results demonstrate that the designed morphing wings can not only accurately achieve the desire airfoil shape, but also simultaneously enhance the actuation efficiency and load-bearing capacity of the morphing wing.