Initially, I think that it has to be made clear that outside of Big Brother and the Party, everyone is weak in Orwell's narrative. The entire purpose for Big Brother's control is to ensure that everyone is weak. The narrative is not one in which men are strong and tough, embodiment of fortitude, and women are demure and weak. Orwell's narrative is too complex for such a reductive reading. In this light, one has to make clear that in discussing the weaknesses of the female characters, men in the novel are just as weak.
Women are shown to be easily controlled by the Party. If a case was to be made that the female characters in the novel are weak, it would start here. Katharine is shown through Winston's recollections as plain and rather dim, someone who is weak of spirit in freely parting from Winston when it is understood that they cannot have children. She is not shown to be strong in the name of her commitment to Winston. Additionally, Mrs. Parsons is shown to be weak and timid because of the fear of her children. The power of her children causes her to be submissive and very weak. Winston's mother was eliminated by the party. Julia's betrayal of Winston was so quick, from O'Brien's point of view, that her weakness was evident. While she professes strength in how she will not betray Winston, we are led to believe that the betrayal was fairly quick. Even the Prole woman, where Winston sees so much of hope and promise for change, turns out to be weak when she runs at the sight of the Thought Police who are there to apprehend Winston and Julia. In these depictions, the argument can be made that the female characters in Orwell's work are shown to be weak. Yet, it has to be stressed again that all of the characters- men and women- are shown to be weakened by the power of Big Brother.