As the previous post states, part of Heathcliff's anger at Catherine is because she chooses to marry the high-class Edgar Linton, rather than Heathcliff, who, as a foundling (perhaps a bastard) is of the lowest of classes.
In Chapter 7, Catherine is forced to spend several weeks at the Linton home recovering from an injury. She returns to Wuthering Heights as a well-mannered, elegantly-dressed lady who seems utterly unfit to be a friend of Heathcliff. Nelly tries to console Heathcliff by telling him that perhaps he is really of high-class birth:
"Who knows but your father was Emperor of China, and your mother an Indian queen, each of them able to buy up, with one week's income, Wuthering Heights and Thrushcross Grange together?..."
"Class" is also a major part of the dislike that Hareton Earnshaw develops for Catherine Linton (the daughter) later in the novel. Hareton should be the master of Wuthering Heights, but he has been reduced by Heathcliff to nothing more than an illiterate servant. When Catherine moves to Wuthering Heights, Hareton is reminded of his low-class status:
He had been content with daily labour and rough animal enjoyments, till Catherine crossed his path. Shame at her scorn, and hope of her approval, were his first prompters to higher pursuits; and instead of guarding him from one and winning him to the other, his endeavours to raise himself had produced just the contrary result.
Heathcliff’s fury erupts after Cathy decides to marry “up” into the world of the Lintons, and not down into the world of Heathcliff.