Ultimately, human responsibility played a greater role in the two lover's deaths. Both chose to disobey their parents and become involved with each other. And both eventually choose death over living without the other. However, there is plenty of blame to go around. Friar Lawrence certainly played a large role when he married the two and when he gave the "temporary" poison to Juliet. In addition, the feuding families bear some of the guilt for continuing a feud that seemed rather meaningless. So meaningless that the deaths of the two lovers forced them to end the feud.
Shakespeare wanted it to show that it was fate that caused the death of Romeo and Juliet , but I believe it's human responsibility . Juliet and Romeo had a choice to not marry each other . They knew that their parents are against it , yet they still chose to love each other .