In harmonic analysis, the Muckenhoupt $A_p$ condition characterizes weighted spaces on which classical operators are bounded. An analogue $B_p$ condition for the Bergman projection was established by Bekolle and Bonami. Recently, weighted norm estimates were obtained for the Bergman projection on various settings. In this talk, I will present sharp estimates for the weighted $L^p$ norm of the projection on a class of pseudoconvex domains. This talk is based on joint work with Nathan Wagner and Brett Wick.