In Disgrace, how is Petrus given power?

Petrus gains power primarily through the acquisition of land. In this remote rural area, land-ownership is a very important indication of social status. The more land you own, the higher up the social ladder you are. And as Petrus starts to expand his land-holdings, he gradually starts to wield more power over Lucy until she eventually comes to realize that marrying Petrus—despite the fact that he already has two wives—might be the only way for her to stay safe.
Petrus's closeness to Pollux—one of the men who raped Lucy and beat up her father—also gives him power. Petrus is able to present himself to Lucy as the only man who can protect her from Pollux. It's almost like he's operating some kind of protection racket: as if he's making an implicit threat. He implies that what happened to Lucy can easily happen again if she doesn't accede to his wishes.

Petrus is a neighbor of Lucy's who is already financially successful at the start of Disgrace. This success is indicated by the amount of land he owns, the amount of livestock he owns, and the number of wives he has.
Petrus' power increases significantly after men come and harm David and sexually assault Lucy. After this incident, Lucy is deeply affected by fear, which prevents her from working her land as effectively as she could. Her fear is exacerbated by the fact that she discovers one of Petrus' cousins was involved in her assault.
As Lucy's power diminishes, Petrus' power grows. He uses her fear to start to take control of her and her land. He starts working the land for her and proposes marriage to her in order to gain further control of her land. When we are first introduced to Lucy, it seems her character would not have agreed to such an offer. However, after the assault, Lucy is so affected that she considers the possibility that marrying Petrus and allowing him to take care of the land would benefit her in that it would provide her with protection.
Therefore, Petrus is given power by Lucy because of her fear and the traumatic effects resulting from her assault.