A good place to start would be Act Two, in which Elizabeth and John clearly display some of the problems that they are experiencing in their marriage thanks to John's infidelity with Abigail. However, relevant to your question is the way that Elizabeth places confidence in the importance John has in the community when she appeals to him to go to town and denounce Abigail Williams openly:
I think you must go to Salem, John. I think so. You must tell them it is a fraud... Let you go to Ezekiel Cheever--he knows you well. And tell him what she said to you last week in her uncle's house.
Clearly Elizabeth feels that her husband is a man of some standing in the community and that his word will weigh heavily with the authorities. This is something that is shown when Proctor and Giles Corey go to Danforth to testify against Abigail and the group of girls that are causing so much trouble.