Tools of Characterization
Either you're in or you're out. Hindley is in and wants to make sure Heathcliff knows it. By excluding, humiliating, and otherwise mistreating Heathcliff, Hindley breeds a resentment that leads to revenge.
Never welcomed into the Earnshaw family, Heathcliff decides to ruin it: he destroys the sanctity of the family and demonstrates no respect for Hindley's wife or son. Being an orphan, Heathcliff has messed up the whole family inheritance thing (although we suspect that he is really Mr. Earnshaw's illegitimate son). Add the fact that Hindley is a trainwreck, and you have a recipe for a hostile takeover.
Being an Earnshaw is good: you get to live in that big house and be a landowner. But being a Linton is even better: Thrushcross Grange is much more cushy, and life with the Lintons is far more pleasant and entitled. That's what draws Catherine over to the Linton side.
But by the end of the novel, the families and houses have, in effect, fused into one.
You would think Emily Brontë could have been a little more creative with her characters' names, rather than recycling the same ones over and over. But that's the whole point. By using the same names—or different combinations of existing ones—for new characters, Brontë creates a feeling of claustrophobia and even incest. The repetition of names also helps tie everything together, as in the case of the two Hareton Earnshaws.
Names are a way of identifying family affiliations (Earnshaw or Linton) and marking those on the outside—as in Heathcliff, who, like Madonna or Cher, has no last name. Heathcliff's name ties him directly to the land rather than a house, which reflects his whole wild-on-the-moors character. Lockwood's name reflects his outsider status and inability to enter. Linton Heathcliff gets a really strange name combination, but since he dies young he is, in a sense, the second and last of the Heathcliffs.
To be a Linton is to have social stature; to be an Earnshaw is to be part of that group of heathens living up on the hill. When Catherine marries Edgar, she changes. All of the names written on her window ledge—Catherine Earnshaw, Catherine Heathcliff, Catherine Linton—represent her different identities.
When this book isn't about love or revenge, it's about social status. We can tell the Lintons are at the top of the local heap: Catherine yearns to marry Edgar in order to become the greatest lady of the neighborhood, and Hindley is only too eager to get the Earnshaws linked up with the Lintons. Though both families are landowners, the Lintons are definitely more refined. Both families are middle class (probably upper-middle class in the case of the Lintons) and, like most middle-class families of the time, both have servants (even if they are surly like Joseph).
Heathcliff starts out on the lowest rung of the ladder: not only does he not have money or property, he has no family affiliation or education. For him, to aspire to any other class would be just plain uppity, and by abetting that rise, Mr. Earnshaw is going against what was perceived to be the natural order of things.
No wonder Hindley is ticked off. Punishment of the sort Hindley inflicts on Heathcliff (and Heathcliff, in turn, on Hareton) hits you right in the social-status groin. By going off with the rogue and usurper, Isabella drags down the Linton family name, which is why Edgar disowns her.