Quote 4
"Oh! you said you cared nothing for my sufferings! And I pray one prayer—I repeat it till my tongue stiffens—Catherine Earnshaw, may you not rest as long as I am living; you said I killed you—haunt me, then! The murdered do haunt their murderers, I believe. I know that ghosts have wandered on earth. Be with me always—take any form—drive me mad! only do not leave me in this abyss, where I cannot find you! Oh, God! it is unutterable! I cannot live without my life! I cannot live without my soul!" (16.25)
To Heathcliff, a life without love is not worth living. In this brief speech, he reveals his anger toward Catherine, which is rare. Usually his rage is directed at any one but Catherine.
Quote 5
"They won't do that," he replied: "if they did, you must have me removed secretly; and if you neglect it you shall prove, practically, that the dead are not annihilated!" (34.81)
If Heathcliff is not buried next to Catherine, he will plague those who refuse his request. Here it is Heathcliff and not Catherine who will be a ghost. And he knows that pretty much everyone else is afraid of ghosts.
Quote 6
"What is it to you?" he growled. "I have a right to kiss her, if she chooses, and you have no right to object. I am not your husband: you needn't be jealous of me!" (11.45)
Just because Heathcliff's not her husband doesn't mean Catherine won't act jealous and possessive of him. In this moment, it's hard not to be on Heathcliff's side.