In 2006, S. Lin and W. Lin introduced the definition of weakly weighted-sharing of meromorphic functions which is between ``CM" and ``IM". In this paper, using the notion of weakly weighted-sharing, we study the uniqueness of nonconstant homogeneous differential polynomials $P[f]$ and $P[g]$ generated by meromorphic functions $f$ and $g$, respectively. Our results generalize the results due to S. Lin and W. Lin, and H.-Y. Xu and Y. Hu.