He [Hindley] has been blaming our father (how dared he?) for treating H. [Heathcliff] too liberally; and swears he will reduce him to his right place. (3.30)
Hindley started the whole revenge cycle by mistreating Heathcliff in the first place. His envy of Mr. Earnshaw's love for the orphan sets off a chain reaction of abuse and mistreatment.
So, from the very beginning, he bred bad feeling in the house; and at Mrs. Earnshaw's death, which happened in less than two years after, the young master had learned to regard his father as an oppressor rather than a friend, and Heathcliff as a usurper of his parent's affections and his privileges; and he grew bitter with brooding over these injuries. (4.55)
Hindley's resentment has a very clear beginning. Before Heathcliff arrives, Hindley is clearly the young man of the house, and he does not easily give up this privilege.
[. . .] they forgot everything the minute they were together again: at least the minute they had contrived some naughty plan of revenge. (6.11)
Catherine helped make the misery more bearable for Heathcliff. She is not only his friend and sister, but his co-conspirator in revenge. Clearly Heathcliff was unwilling to sit back and accept poor treatment, even as a child.
I'm trying to settle how I shall pay Hindley back. I don't care how long I wait, if I can only do it at last. I hope he will not die before I do! (7.69)
Even early on, Heathcliff's desire for revenge competes with his love for Catherine. Revenge is one of the emotions that drives Heathcliff and gives him a reason to live. The fact that Hindley dies before Heathcliff allows him to inherit Wuthering Heights.
It expressed, plainer than words could do, the intensest anguish at having made himself the instrument of thwarting his own revenge. (9.12)
Rescuing Hareton from death, Heathcliff recognizes that his instincts prevented the perfect punishment for Hindley—the death of his heir. Because he rescues Hareton, Heathcliff has to work a lot harder to get back at Hindley.
I meditated this plan—just to have one glimpse of your face, a stare of surprise, perhaps, and pretended pleasure; afterwards settle my score with Hindley. (10.60)
Heathcliff is driven unequally by two aims: love and vengeance. Catherine knows that Hindley deserves Heathcliff's vengeance (because she was a victim of it as a child), and so she never intervenes on his behalf.
"I seek no revenge on you," replied Heathcliff, less vehemently. "That's not the plan. The tyrant grinds down his slaves and they don't turn against him; they crush those beneath them." (11.51)
Though Catherine perhaps deserves punishment for turning against him, Heathcliff would do no such thing. What's notable here is that Heathcliff recognizes a pecking order: people pick on those beneath them.
"Oh, damnation! I will have it back; and I'll have his gold too; and then his blood; and hell shall have his soul! It will be ten times blacker with that guest than ever it was before!" (13.63)
Hindley loses everything to Heathcliff but must partly blame his own weaknesses and indulgence. He aspires to rob Heathcliff of everything and, like a devil figure, even wants his soul.
He had the hypocrisy to represent a mourner: and previous to following with Hareton, he lifted the unfortunate child on to the table and muttered, with peculiar gusto, "Now, my bonny lad, you are mine! And we'll see if one tree won't grow as crooked as another, with the same wind to twist it!" (17.119)
With Hindley dead, Hareton is left to suffer under Heathcliff. Like others who fall victim to Heathcliff's abuse, Hareton is a proxy for his father. That Hareton breaks the cycle is a reflection of his love for Catherine and his own strength of character.
It is a poor conclusion, is it not . . . An absurd termination to my violent exertions? I get levers and mattocks to demolish the two houses, and train myself to be capable of working like Hercules, and when everything is ready, and in my power, I find the will to lift a slate off either roof has vanished! My old enemies have beaten me; now would be the precise time to revenge myself on their representatives: I could do it; and none could hinder me. But where is the use? I don't care for striking. I can't take the trouble to raise my hand! That sounds as if I had been labouring the whole time, only to exhibit a fine trait of magnanimity. It is far from being the case—I have lost the faculty of enjoying their destruction, and I am too idle to destroy for nothing. (33.59)
All of the scheming, anger, and brutality have finally exhausted Heathcliff. At the culmination of his plot, he no longer has the desire to see it through. As a result, the spell is broken, and peace can return to Wuthering Heights.