Gravitational centers of precise spinning components must coincide with the rotational centers of those to reduce noise and vibration and to extend those lift as well. Therefore quality control should be performed in the manufacturing process, in which the unbalance moments are accurately measured. In this paper 3-point weighing method is adopted to measure the unbalance moment of small-sized precision spinning elements using electronic scales with 0.1 mg resolution. Firstly methods to eliminate the fixture error and to reduce the effects of frictional force that is known as side effect, are proposed. A measuring system is developed and various experiments are performed to verify the proposed approach. The measured and calculated values are analysed in statistical methods, and this provides the errors of the measuring system. The results show that the proposed theory and test procedures gives reliable unbalance moments and gravitational centers.