He sees her more often that he doesn't. Whether it's in his mind, through the warlock, or in person, she's usually on his mind. The normality with which she lives, despite the constant supernatural interference, intrigues him. And he finds himself checking in on her more often that strictly necessary.
He uses her aunt's invitation to his advantage constantly, and there are many nights she gets back from seeing Stefan to find him in her bedroom, sitting underneath her window, unseen by anyone outside—not that he's afraid of her Salvatore protectors, but he'd rather not deal with them if he can help it.
By unspoken agreement, she doesn't speak of his visits to aforementioned protectors. For some reason, she trusts him in his deal to keep her out of danger, as that's what he wants at the moment. So she figures he's not there to do anything harmful.
Sometimes he asks her questions. Usually he only asks about the mundane—about school, or her friends, or her family—but sometimes about Stefan or Damon. Sometimes he just sits there and watches her do homework or write in her journal, which he promised one night that he'd never read. Sometimes, the roles reverse, and she asks questions of him—of vampires and the hierarchy, his past, what he knows of Stefan or Damon or even Katerina. And sometimes she just lies on her bed and stares at him.
Somewhere along the line, he finds himself wavering in his original plan to use her for his intended purpose, and cares little for his deal with her. He just likes sitting there, underneath her window, experiencing a little taste of normality with her—what life could be like if she wasn't so attached to her Salvatore protectors.
But he vows, one night, as she sleeps, that one day those Salvatores will fade in importance, and he'll still be here, watching her sleep.