Thin-walled structures with weak stiffness are widely applied in aerospace, precision machinery, and mold manufacturing; however, their machining processes are commonly challenged by insufficient rigidity, complex dynamic characteristics, and a high susceptibility to chatter. Due to the differentiated dynamic parameters of these structures at various spatial positions, the compliant interaction between the tool and workpiece during milling significantly increases the risk of chatter, thereby degrading machining precision, surface integrity and productivity. To this end, this research establishes a three degree of freedom (3-DOF) milling process dynamics model based on the full discretization method (FDM), which systematically obtains the modal parameters of the thin-walled component at different locations. Building upon this, position-dependent stability lobe diagrams for milling prediction are constructed to theoretically reveal the influence of local structural regions on milling stability. Furthermore, this paper proposes a multivariate nonlinear regression method to establish a nonlinear identification model for milling force coefficients. Key parameters were effectively identified through experiments, predicting the variation trends of force coefficients under different cutting conditions. Subsequently, cutting experiments were conducted across different spatial regions of the thin-walled structure to comparatively analyze stability performance under various combinations of cutting parameters. The results demonstrate that the established dynamic model and force coefficient identification method can effectively predict the milling stability of weak-stiffness structures at different physical locations and can well explain the spatial distribution characteristics of cutting chatter. This research proposes a novel method for position-dependent milling stability prediction, providing a theoretical foundation and experimental data support for resolving the issue of frequent chatter at different locations on weak-stiffness structures in practical machining, which holds significant engineering value for the efficient and stable processing of complex thin-walled components.