There are no written text specifying the responsibilities of a Brother towards His sisters, including the Manusmriti.
However, there are practices being followed in Hindu Households by way of tradition.
1.Brothers would get married only after the sister is married, even if he is a younger brother..
2.In a Hindu household, the eldest, if he happens to be a Male, is next in charge of the House and as such has the responsibility of taking care of his sisters.
3.In the event of father being deceased, the brother is regarded the Father and his duties towards his sister is that of a Father to his daughter.His wife, even if the Father is alive, is the Mother to all his siblings and she is to be accorded the respects as that befits a Mother.
Maternal Uncle is the person who performs the Karna Bhushana(Ear piercing ceremony of the child) and the first hair tonsuring of the child and during Upanayana and Marriage, he plays an important role.
5.The sister is to brought to the Brother’s Home, of Father is not alive, to look after her during pregnancy.
6.The status of a maternal Uncle is very high in Hinduism.In fact he occupies a position not enjoyed by the parents of the child or Grand[parents.
7.There used to be a custom that the right of marrying sister’s daughter rested with the maternal Uncle.Even now, in certain communities, this custom is followed.
8.In every function, the sister and her husband are to be given special respects.
9.In the unforeseen event of the sister’s husband passing away, looking after the Family of the sister is the responsibility of the brother.