How can I prove the following statement in The Crucible: "This play centers on courage, weakness and lies."
In all honesty, I don't think you are going to have a difficult time in suggesting that the statement is true. The play is about courage. Cite the examples of Proctor, Elizabeth, and Giles Corey as representative of this. The conclusion of the play reflect Proctor's courage in upholding "his name" and the idea that contingent circumstances should not define an individual in the face of transcendent reality. The fact that his wife stands with him is another example of courage, reflected in her willingness to "not take his goodness from him" at the moment he has achieved it. Giles Corey's courage to not name names at his own cost because of his willingness to "not bring harm to another" is courage. The fact that he endures his punishment with the charge of "More Weight" to reflect this is another example of courage. To a lesser extent, Hale's willingness to stand up to the court when he knew it was wrong could also be seen as an example of courage in the drama.
The play is also about weakness. In this, I would cite Mary Warren's inability to stand up to Abigail and the girls during the trial. She is incapable of being alone and being apart from her social condition, even if this means that there has to be a sense of sacrificing morals and ethics to do so. I would also cite Proctor's own weakness with his affair and the inability to take action from the start of the drama. Proctor's own weakness helps to perpetuate the drama, and, in a sense, his own suffering. Finally, the weakness of the town has to be evident in that few, if any stands up for what is right. I think that Miller makes this clear that the lack of courage of the town is what enables the trials to reach such a fevered pitch with such grave consequences.
Finally, Abigail Williams represents the embodiment of lies and deception that helps to formulate the crux of the drama. Abby's willingness to spin lies in any condition to get her way is a part of the drama. The consolidation of the girls' friendship through lies and deceit is another part of such a reality. This behavior is seen in Parris, who is more concerned with consolidating his own power, and in Danforth and Hathorne, judges who would be more concerned with suborning perjury than obtaining the truth if it would bring discredit to their trials and proceedings. I think that this becomes something extremely important to the construction of the drama.