This paper presents application of a numerical analysis method to investigating the sound insulation performance of membranes with additional weights (MAW), and furthermore, clarifies the mechanism of the high insulation effect of MAW through a theoretical discussion. The MAW has been recently developed in order to improve low insulation performance of ordinary membranes in the low frequency range, however, the mechanism of its remarkable effect is not clear at the moment. The numerical method applied is a general vibro-acoustic coupling analysis method for membrane materials, in particular, taking into consideration loaded mass and air permeability, which is derived from a series of our studies on prediction of sound insulation performance of building elements. The numerical results show that the insulation effect of MAW occurs at low frequencies independently of the incident angle of a sound wave and of the boundedness of MAW, and also clarify the influence of each property of MAW on the peak frequency of transmission loss and the frequency range of high insulation performance. Subsequently, in view of the above results a infinite-sized MAW model is addressed, and the peak frequency of transmission loss is approximately formulated in the simple form. The formulation proves that the insulation effect of MAW occurs independently of the incident angle and the boundedness. In addition, it is confirms that the formulated peak frequency favorably agrees with the actually obtained peak frequency on condition that it is lower than the natural frequency of the fundamental mode of the divided area by weights. As a result, it is concluded that the insulation effect of MAW is caused by the interference between the two vibration component, that is, of the progressive bending wave and of the fundamental mode in the divided area.