We investigate the intensity effect of ultrashort assisting infrared laser pulse on the single-XUV-photon double ionization of helium atoms by solving full six-dimensional time-dependent Schrtdinger equation with implement of finite element discrete variable representation.The studies of joint energy distributions and joint angular distributions of the two photoelectrons reveal the competition for ionized probabilities between the photoelectrons with odd parity and photoelectrons with even parity in single-XUV-photon double ionization process in the presence of weak infrared laser field,and such a competition can be modulated by changing the intensity of the weak assisting-IR laser pulses.The emission angles of the two photoelectrons can be adjusted by changing the laser parameters as well.We depict how the assisting-IR laser field enhances and/or enables the back-to-back and side-by-side emission of photoelectrons created in double ionization process.