Heathcliff is both a hero and a villain. At different times in the book and with various characters, he has the potential to be a hero. At other times and with other characters, he is a villain. He starts out young and good, with the possibility of becoming the story’s hero in the traditional sense of the term.
After he endures belittling treatment from Hindley, who turns him into a servant, and overhears Cathy tell Nelly that it would degrade her to marry him, Heathcliff becomes a tormented character. Deep inside, Cathy senses that it will be wrong for her to marry Edgar Linton:
It would degrade me to marry Heathcliff now; so he shall never know how I love him: and that, not because he’s handsome, Nelly, but because he’s more myself than I am. Whatever our souls are made of, his and mine are the same; and Linton’s is as different as a moonbeam from lightning, or frost from fire.
After this, Heathcliff leaves Wuthering Heights. When he returns, he exacts his revenge on the people he believes contributed to ruining his chance for happiness. He becomes dark and vengeful, turning to become the villain of the story as he reacts to the treatment he has received from other characters. However, until the very end, he remains true to Cathy and is the hero of the story of just Heathcliff and Cathy. He acknowledges how villainous he is when he says to Catherine,
to you I’ve made myself worse than the devil. Well, there is ONE who won’t shrink from my company! By God! she’s relentless. Oh, damn it! It’s unutterably too much for flesh and blood to bear even mine.
By "ONE," he is referring to Cathy, who haunts him even after her death. He remains her hero despite all the horrible things he has done to other characters in the book.
Heathcliff is a hero in the broadest sense of the word because he is the chief character or protagonist of the novel. He is not, however, a hero in the strictly tragic sense like Hamlet or in the exalted sense of a noble war hero. He probably most resembles an archetype known as the "Byronic hero," who became a literary fixture during the Romantic era. This hero is not necessarily likeable, noble, or kind. Rather, he is a tortured wanderer who tends to think mostly of himself. This hero was modeled after Lord Byron, and one famous Byronic hero is Victor Frankenstein.
Heathcliff is neither; he is an anti-hero. For, he possesses qualities of the hero: loving, courageous, physically strong, with imperfections such as feeling overpowered by his obsessive and thus selfish love. Heathcliff feels forces him into certain actions, living only to prove his worth to his beloved Cathy. While he becomes the master of his foster brother buying up the old home--and cruelly treating him--Heathcliff remains the slave of his love to Cathy, ever brooding over her, and marries her sister-in-law only to be close to Cathy.
After Cathy dies, Heathcliff does not abandon his love for her, a testimony to the genuineness of his feeling. But, again the love is not heroic. Rather it is yet obsessive: Heathcliff wakes to the ghost of Cathy, he fails to care for himself, living only to be reunited with the woman who gives him his soul.
In a sense Heathcliff is merely a darker side of Catherine who herself is self-centered and fickle. For, does not Catherine at one point in the novel excalim, "Heathcliff is I"?
Heathcliff is a villain in Wuthering Heights. He is a sympathetic villain, but nevertheless a villain.
Bronte builds our sympathy for him by allowing us to catch glimpses of his childhood, and we feel for him because of the way Hindley abuses and degrades him. We also feel the intensity and sincerity of his love for Catherine, which humanizes him in our eyes.
We understand Heathcliff's pain because we have witnessed his childhood and know very well that he was influenced by a warped patriarchy. He did not start out bad, but was made bad. As Brontë wants us to understand, his society puts too much power into the hands of the dominant male in the family. Society stands by and accepts the alcoholic Hindley's unchecked power to ruin Heathcliff's life. We also feel for Heathcliff's deep anguish when Catherine dies.
However—and this is Brontë's point—Heathcliff learns his patriarchal lessons all too well. He becomes a gentleman during his three-year absence and turns the weapons of patriarchy against his enemies. He becomes the male with too much power, and he knows, from the experience of how he was victimized, that he can use it against others unchecked.
When Catherine dies, Heathcliff loses his tie with the one person who can humanize him. After her death, he becomes ruthlessly cruel. There is a tendency to see him a a Byronic hero and a romantic "hunk," as Isabella does, but Bronte makes it relentlessly clear that no amount of human kindness runs beneath his hard exterior.
He abuses his wife Isabella, abuses his daughter-in-law Cathy (for example, in one scene he holds her hands in one hand and repeatedly slaps her face), degrades Hareton as he himself was degraded, is manipulative and cruel to the son he despises, and tyrannizes and terrifies his household. Brontë wants readers to see him as a villain and as a representative of patriarchy run amok.
Heathcliff would certainly be classified as a villain over a hero but that does not mean that he is completely evil and does not warrant sympathy. When Heathcliff is a child, Mr. Earnshaw finds the orphaned boy alone in the streets of Liverpool. Mr. Earnshaw adopts him, yet he is not considered an equal in the family due to his dark skin and assumed low-born origin. Heathcliff has a wild spirit and an insolent temper, and he is quick to anger. He grows up playing with Cathy on the moors surrounding Wuthering Heights and grows to love her. Heathcliff becomes jealous when Cathy is courted by the wealthy Edgar Linton.
Realizing he is not suited to marry Cathy, Heathcliff leaves Wuthering Heights for three years to obtain a fortune. Heathcliff returns shortly after Cathy marries Edgar Linton. Heathcliff is crushed by this betrayal, and both he and Cathy are tortured by their passionate love that cannot be. Cathy dies giving birth to Edgar's daughter, who is also named Catherine. Heartbroken over Cathy's death and how he had been unable to marry her, he becomes consumed with getting revenge on both the Lintons and the Earnshaws.
The novel's second section takes place a generation later. When Cathy's brother Hindley dies, Heathcliff gains possession of Wuthering Heights and takes in Hindley's orphaned son Hareton. Heathcliff treats Hareton poorly, making him labour on his own family's property, denying him a proper education, and verbally abusing him—he is determined to treat Hareton worse than Hindley had treated Heathcliff when they were growing up.
After Edgar Linton dies, Heathcliff sets his sights on depriving the young Catherine's ownership of Thrushcross Grange. He manipulates her into marrying his sickly son Linton, and when Linton dies, Heathcliff acquires Catherine's fortune. She is forbidden from leaving Wuthering Heights, and Heathcliff treats her in the same despicable manner as Hareton.
Heathcliff's redeeming quality is his intense devotion to Cathy and the love he bears for her until the end of his life. Heathcliff is haunted by her untimely death and sees her ghost multiple times. Though his vengeful actions are inexcusable, readers have a certain degree of sympathy toward him, as he was prevented from being with the woman he loved simply because he is low born. Heathcliff is considered an anti-hero because he is neither a complete villain or a hero. He does possess some heroic qualities: including love, courage, devotion.