The phenomena of variability and interference in the natural frequencies of weight-sensing structures applied in complex working conditions must solve the problem of reducing or eliminating resonance under low-frequency vibrations to maximize stability, accuracy and reliability. The influence laws of the additional mass with relevant characteristics on the natural frequencies, which include the components of mass, stiffness and center-of-mass distribution, etc. Firstly, the theoretical formulas of the mathematical model are given based on different characteristics of the weight-sensing structure, and various combinations of additional masses on the weight-sensing structures are adjusted in the X-, Y-, and Z-directions. The key factors to be specifically considered in the theoretical formulas are discussed through simulation analysis and experimental validation. Secondly, the locking strength of the fastening screws of some components was changed, and another component was placed on the experimental platform in the experiment. The results show that the mass, center-of-mass, stiffness distribution and other factors of the additional mass have different effects on the natural frequencies, which are important for the demand for high-precision, high-stability weighing measurement. The results of this research can provide an effective scientific evaluation basis for the reliable prediction of natural frequencies.