Who was the disciple that Jesus referred to on the cross?

in John 19:26-27 Jesus said to one of the disciples standing nearby " Son, Behold your Mother". Who was the desciple that he was referring to? I understand that he loved John more (correct me if i'm wrong) but I've always thought that Peter was the head of the disciples? And in Jewish culture, it is a custom to "handover" the members of the family to the next elder brother, supposed that the eldest had gone, Right?? and if so, why didnt he "handover" Mary to Peter considering if Peter was the head of the congregation ?