Ultra-weak fiber Bragg grating (UWFBG) array-based phase-sensitive optical time-domain reflectometry (Φ-OTDR) utilizes the interference interaction between the reference light and the reflected light from the broadband gratings for sensing. It significantly improves the performance of the distributed acoustic sensing system (DAS) because the intensity of the reflected signal is much higher than that of the Rayleigh backscattering. This paper shows that Rayleigh backscattering (RBS) has become one of the primary noise sources in the UWFBG array-based Φ-OTDR system. We reveal the impact of the Rayleigh backscattering signal on the intensity of the reflective signal and the precision of the demodulated signal, and we suggest reducing the pulse duration to improve the demodulation accuracy. Experimental results demonstrate that using light with a 100 ns pulse duration can improve the measurement precision by three times compared with the use of a 300 ns pulse duration.