At one point, Catherine even says, "It would degrade me to marry Heathcliff" (Bronte, p. 73). Although she could not and would not marry Heathcliff, it is apparent they love each other. This leads to a bit of jealousy on Edgar's part when they are married. As an act, he is always trying to keep Catherine and Heathcliff apart, resulting in verbal and physical violence when he sees them together.
To Edgar's extreme disapproval, Isabella, his sister, eventually becomes attracted to Heathcliff. The two soon run off to get married. When Nelly asks Edgar to "rescue" Isabella from elopement, he refuses to do so. It turns out that Heathcliff is only using Isabella to anger Edgar. This leads to the mistreatment of Isabella and thus, she's stuck in a miserable marriage. There were several occasions where Isabella asked for forgiveness from her brother, however, was turned down. When Edgar found out about Isabella and Heathcliff's marriage, he refused to retrieve her and said, "Hereafter she is only my sister in name: not because I disown her, but because she disowned me" (p. 122). Edgar is apparently getting some sort of revenge by not even willing to rescue his own sister from an apparent mistake. In chapter 13, Isabella wrote a letter to Edgar, asking for an apology and forgiveness. However, Edgar did not reply. Again, Edgar is obviously so mad at Isabella to the extent that he does not really care how she is being treated by Heathcliff.
Catherine Earnshaw, involved in a "love triangle" with Heathcliff and Edgar, also becomes extent on revenge. First of all, when she finds out that Isabella has become attracted to Heathcliff, her reaction is obviously one out of jealousy and selfishness. Although she will not marry Heathcliff, she apparently wants him to herself and is angry that Isabella is falling in love with him. She explains to Isabella that Heathcliff is not a good person to fall in love with and that he"d "crush her like a sparrow's egg" (94).