Inspired by natural morphogenesis, controlling the shape of soft materials through differential growth has emerged as a strategy for developing smart devices. However, existing theoretical models typically neglect body forces (e.g., gravity), thereby restricting their applicability. Furthermore, mainstream inverse design methodologies rely on computational strategies, such as optimization and machine learning, but often lack mechanistic transparency compared to closed-form relations. To address these limitations, this study establishes a framework for shape control of hyperelastic plates that accounts for body forces. A key contribution of this work is the derivation of explicit asymptotic analytical solutions to the inverse problem. Unlike ``black-box'' numerical approaches, these solutions reveal quantitative relationships among applied body forces, required growth functions, and the geometric properties of the target shapes. We propose a shape-control framework that calculates analytical expressions of growth fields and designs appropriate loading paths to suppress structural instabilities. Our work demonstrates that body forces are not merely external loads but can also be harnessed as beneficial factors for shape morphing. The theoretical results are validated through three-dimensional finite element simulations and experiments on silicone plates under self-weight, demonstrating good agreement. This research provides mechanical insights and a design tool for morphing systems, extending the scope of soft robotics and deployable structures to scales where body forces are significant.