In this paper, we introduce the definition of weakly weighted-sharing which is between ''CM'' and ''IM''. Using the notion of weakly weighted-sharing, we study the uniqueness problems on meromorphic function and its kth order derivative f ðkÞ satisfying certain sharing set properties. As consequences, we are able to answer questions posed by Kit-wing Yu, which were also studied by I. Lahiri and A. Sarkar, L. P. Liu and Y. X. Gu. Our results sharpen the above results.