Just about everyone in Wuthering Heights suffers physical and emotional trauma, and many of them even die from it. Heathcliff avoids physical illness, but his love for Catherine causes an extraordinary amount of suffering, both for himself and others. He seems to enjoy the suffering, pleading to be haunted by her after her death.
No one really wants to take responsibility for the misery that results from his or her own foolish decisions – including silly Isabella, who marries Heathcliff knowing he doesn't love her. No suffering surpasses that of Heathcliff and Catherine, and still they blame each other. One of the last things Heathcliff says to Catherine, as she lies dying in his arms:
"Misery, and degradation, and death, and nothing that God or Satan could inflict would have parted us, you, of your own will, did it. I have not broken your heart – you have broken it – and in breaking it, you have broken mine." (15.37)
He does have a point there.
Suffering is central to Catherine and Heathcliff's expression of love. Without being miserable, their characters would not be as provocative to each other or to the reader.