|Love story? Not likely.|
So lets look at the conventions of a romance and try to see how Wüthering Heights might fit into these, if at all. A romance usually has three stages. Towards the beginning, two characters meet and fall in love. Obstacles then arise preventing them from being together. Finally at the conclusion of the novel these challenges are overcome so the protagonists can be together. If we really wanted to Wüthering Heights could fit into some but it's not an easy task.
At the beginning of the novel Cathy and Heathcliff meet, but it's hardly love at first sight. Although this may not be much of a problem (Lizzie Bennet and Mr. Darcy are closer to hatred than love at first sight) the pair never really fall in true love. Heathcliff may have fell for her, but Cathy never acted as if she loved him. She delighted in tormenting both him and Linton and exploiting them to gain her every whim and desire.
So they don't really match the first criteria for a romance, but what about the other two. Obstacles do arise, but these aren't external character or other factors. The obstacles are Cathy's selfishness. Nothing else. There were plenty of opportunities for the pair to be together, but her need for attention and wealth led to her marrying Linton. At this point she could have let Heathcliff go and move on but she continued to want his company and forcing him to stay (I finally see the parallels to Twilight). Still, if they managed to get together in the end the novel might still be a romance, but they don't. Cathy dies mid-way through the novel still trying to manipulate Linton and Heathcliff against each other.
Looking less at the content and structure, lets look at the characters. Traditionally the central couple of a romance are likeable, even if the supporting cast are detestable (think Romeo and Juliet). With Wüthering Heights the opposite is true. Although no character is really anyone you'd like to be friends with the peripheral characters, at least have some redeeming features. Cathy and Heathcliff themselves don't. Cathy is selfish, manipulative and greedy, whilst Heathcliff is cold, cruel and to an extent murderous (although at least he was made that way by neglect as a child and Cathy's manipulations). I think you'll agree that even if they're not at the beginning, by the time both dies they are monstrous. They're not characters you want to fall in love and live happily ever after. Not in the slightest.
If this is true, then why do people see the novel as a "romance" or the more apt description of a "gothic romance"? The only plotline in the novel which resembles a romance is Cathy Jr. and Hareton and even that's barely a love story. So please can why just give Wüthering Heights the label it deserves and call it simply "gothic". I'm sure when Miss Brontë wrote the heights, she did not intend for it to be a romance and certainly not for Heathcliff to be seen as a hero which women fell in love with. It's an exploration of evil and the darkness in side of humanity. Not a love story.
Afterthought: I may have been a little harsh on Cathy but I'm not sorry. I really didn't like her.