A Boolean function with good cryptographic properties over a set of vectors with constant Hamming weight is significant for stream ciphers like FLIP. Efficiency is another critical criterion for designing a stream cipher. The nonlinear filter function used in the cipher FLIP is a direct sum of three Boolean functions to be efficient with a high number of state variables. In our work, we have studied the construction of WAPB and WPB Boolean functions by the direct sum of two WAPB/WPB Boolean functions. A general result in this direction is presented. We have presented some cases when the direct sum results a WAPB/WPB Boolean function. We have introduced several constructions of WAPB/WPB Boolean functions in this context. Some results on the direct sum of WAPB/WPB Boolean functions presented by Carlet et al. in IACR Trans. Symmetric Cryptology 2017(3) and Zhu et al. in Discrete Applied Mathematics 2022(314) are direct consequences of the obtained results.