A laser interferometer will be used in the spaceborne gravitational-wave detection missions to measure the inter-satellite optical pathlength variations. The phase readout system of the interferometer needs to be carefully designed and tested to accomplish a shot-noise-limited detection performance under the situation of pico-Watt level received lights. In this work, a scheme based on dual-tone acousto-optic diffraction is presented to verify the performance of the weak-light phase readout system. By optimizing the parameters of the photoreceiver and the local strong-light power, the signal-to-noise ratio of the beat-note signal is enhanced. Thanks to the scheme's common-mode noise rejections for the laser frequency noise, and the optical-path noise, etc., the differential phase noise has achieved a performance of 2×10-4 rad/Hz1/2, which is dominated by the weak-light (∼13 pW) shot noise above the frequencies of 2 mHz.