As a Byronic hero, Heathcliff's nature is intrinsically connected to his tormented, inhumanly passionate love for Catherine Earnshaw. Catherine, too, loves him passionately, "He's more myself than I am....I am Heathcliff. Heathcliff is her one unselfishness; yet, she rejects him to follow convention and marry her cousin.
When Heathcliff, whose arrogant nature that lacks any heroic virtue, returns to wreak revenge upon both Hindley and Catherine--the only fit justice for rejection--Catherine tells her sister-in-law, "He's a fierce pitiless wolfish man...and he'd crush you like a sparrow's egg..." Catherine warns Isabelle. As she lies dying, Catherine tells him that he has driven her mad. Then, after Catherine dies, Heathcliff prays her soul will know no rest because he "cannot live without my life, I cannot live without my life."
Sharing a fierce, tormented, primal love, Catherine and Heathcliff are lost to each other, each possesses the spirit of the other. But, when they are torn apart, Heathcliff destroys them both in his Byronic revenge. Catherine loses her passion and dies; Heathcliff no longer has "his life,,,,[his] soul" and, too, dies, but looks as though carried off by the devil.
As Shakespeare cautioned, violent delights often have violent ends.
The nature of love in Wuthering Heights is a disappointing one. Heathcliff's obsession with his love to Catherine drives him insane where it started just to get back at Edgar for taking Catherine away from him but it becomes so much more than that. Remember that the only reason Heathcliff married Isabella was to get revenge on Edgar. Isabella writes in a letter to Nelly how Heathcliff blamed her for the death of Catherine and treats her wrongly. Heathcliff's thirst for revenge last so long that he ends up forcing little Cathy into marrying his son which ends badly. In the end Heathcliff realizes that revenge was so tasteless and confess to nelly how he no longer seeks it. You can really tell that Heathcliff is starting to wind down when he looks at little Cathy and see her mother in her face and he is reminded of the he had for her mother.
Catherine and heathcliff have an everlasting passionate relationship with one another and they play behind eachothers backs for revenge