With the help of weighted sharing of sets, we find out the class of meromorphic functions $f$, when $P(f)$ and $[P(f)]^{(k)}$ share a set $\mathcal S_m$ of small functions. Our results improve and extend the results of Zhang and Yang [Ann. Acad. Sci. Fenn. Math. extbf{34} (2009), 249--260] and Xu et al. [Rev. Mat. Teor. Apl. extbf{23}(1) (2016), 291--308]. A number of examples are exhibited to validate certain claims of the main results.