A tragic hero has several characteristics which Heathcliff clearly demonstrates. For example, a tragic hero has a tragic flaw, which is one fundamental flaw in his or her character which, more than anything else, is responsible for his or her downfall. Heathcliff's tragic flaw is arguably his love for Catherine Earnshaw. This love is all-consuming and ultimately destroys him. In chapter 16, after Catherine's death, Heathcliff "dashe[s] his head against [a] knotted trunk" and "howl[s]... like a savage beast being goaded to death with knives and spears." He screams that he "cannot live without [his] life... without [his] soul!" Heathcliff allows his love for Catherine to define him entirely. It is his reason for living—so much so that when she dies, he feels it as his death, too.
A tragic hero also usually evokes feelings of pity and fear. Heathcliff is a tragic hero by this measure, too. Indeed, we pity him when he is a boy because he is tormented and abused by Hindley. Catherine writes in her diary that Hindley's behavior toward Heathcliff is "atrocious," and indeed, Hindley relentlessly beats, degrades, and humiliates Heathcliff. In fact, Hindley degrades Heathcliff so much as to make it impossible for Catherine to marry him.
Heathcliff as a man, however, inspires more fear than he does pity. He humiliates Hareton as Hareton's father, Hindley, humiliated him. He also treats his wife, Isabella, with despicable cruelty and utter disdain. Isabella says in chapter 13 that "a tiger or a venomous serpent [cannot] rouse terror in [her] equal to that which [Heathcliff] awakens."