Since grandma wanted to get in Peter (posess his body after she died), why was his sister her favourite (as stated by her mother) and not him? Why weren't they closer (like for example his sister was with grandma)?
Based on how I understood the movie, Peter's grandma was part of the cult, while ever since Annie allowed Charlie near her, Charlie was possessed by Paiman. Grandma worshipped Paiman, Paiman is in Charlie, so it follows that Charlie was grandma's favorite.
That said, as Charlie mentions in the movie, her grandma would have preferred she was a boy, as it would be more fitting for the demon she's hosting. That's why the events of the movie transpire—it's just a plot to get Paiman into a male host.