High-precision parameter estimation plays an important role in modern science and technology. Quantum weak measurement is a technique that can be used to amplify and estimate small parameters. It is of great significance to explore the influence of quantum weak measurement on the precision of parameter estimation. The weak measurement process mainly involves two physical systems: the system and the pointer. This process consists of three main steps: first, preparing the initial state of the system and the pointer; second, the system weakly interacts with the pointer; third, the system is postselected to a final state that is nearly orthogonal to its initial state. Many factors affect the estimation precision of the coupling parameters. In this paper, the influence of the initial state parameters of the pointer (mean and variance of coordinate distribution), coupling constant and post-selection angle on the estimation precision of the coupling parameters are investigated when the spatial degree of freedom and polarized degree of freedom of the beam are coupled through a birefringent crystal. We specifically discuss the influence of relevant parameters on the Fisher information of coupling parameters to be estimated, and analyze the influence on the estimation precision of coupling parameters. The results show that (1) increasing the variance and the mean value (the center position) of the initial state coordinate distribution can improve the post-selection probability and increase the total Fisher information; (2) The smaller the coupling constant, the higher the estimation precision, but the lower the corresponding post-selection probability; (3) Under the condition of weak measurement approximation, the more orthogonal the post-selection state and the initial state of the system are, the higher the estimation precision is. Therefore, we can obtain larger Fisher information about the parameters to be estimated by appropriately adjusting these tunable parameters, that is, to improve the estimation precision of the coupling parameters.