Concerning a question of Yi [18], we study the problem of uniqueness of meromorphic functions sharing two sets with the notion of weighted sharing of sets and obtain four results which will not only improve the results of Lahiri [12], Lin-Yi [20] but also improve a recent result of the present author [3] and thus provide an answer to the question of Gross [6] in a more compact and convenient way. We exhibit two examples to show that a condition in one of our results is sharp. Till now our result is the best in this regard.