We have explored the effect of weak magnetic field on the transport of charge and heat in hot and dense QCD matter by calculating their response functions, such as electrical conductivity, Hall conductivity, thermal conductivity and Hall-type thermal conductivity in kinetic theory approach. It is found that the electrical and thermal conductivities decrease, and the Hall and Hall-type thermal conductivities increase with the magnetic field in the weak magnetic field regime, whereas the emergence of finite chemical potential enhances these transport coefficients. The effects of weak magnetic field and finite chemical potential on aforesaid transport coefficients are more noticeable at low temperatures, but high temperature suppresses these effects. As a result, some observables associated with the aforesaid transport coefficients such as the Knudsen number, the elliptic flow etc. are most likely to be affected by the magnetic field.