First, you need to make sure that you fully understand the characteristics of Romantic literature in nineteenth-century England.
Basically, the Romantics believed that man, as an individual, is superior, so Romantic novels really probe deeply inside characters. You can see this most obviously in Heathcliff, with his rage and jealousy, and also in Catherine, with her need to conform to social standards and her willful stubbornness.
The Romantics played up emotion before logic. Therefore, many of the characters' actions are inexplicable, such as Heathcliff's treatment of Hareton and Linton or Catherine's outburst at Heathcliff on her deathbed.
The Romantics were also suspicious of previous versions of organized religion. We can see this in the novel through the scenes that depict the Earnshaw children being taught their Bible lessons. The teacher is frustrated at how the children are not listening—even Hindley is not interested.
Beyond that, many people feel that this novel contains characteristics of a Gothic Romance. In addition to the Romantic characteristics, gothicism includes "ruin, decay, death, terror, and chaos, and privileged irrationality and passion over rationality and reason." Certainly we can see these elements in the novel in addition to the gothic elements of nightmare, supernatural elements, and mysticism.
The heath is a desolate place, and Wuthering Heights itself is a dark and dreary place. Death certainly occurs in abundance, leaving only a few characters alive at the end. Nearly all the characters act and react irrationally, especially Heathcliff and Catherine as it concerns their own relationship. The ghost of Catherine that "greets" Lockwood is an example of a supernatural occurrence.
Search for passages that meet these characteristics, and you will have a terrific paper!