This type of attachment—amounting almost to an obsession—is not uncommon in young children. Sometimes it is directed to an older child of the same gender rather than the opposite, as with your daughter. If I may be personal, this sort of thing happened to me in reverse when I was an adolescent. An adorable little 4-year-old girl in the small town where I grew up became quite fixated on me, told everyone that she was my “little girl,” named all her dolls “Bettye Ruth” and even wanted to change her name to mine. I spent time with her when I could, but, as we lived a good distance apart, this was not often possible. Even so, it lasted for several years. But eventually I moved away, and she grew up. I don’t know whether she even remembers me now, although I remember her quite fondly—and remember being complimented by her attachment to me. I don’t think she was in any way harmed by her fixation. So I would suggest that you include Billy in family activities when you can, but make certain both he and your daughter understand there are limits to how much time he can stay around. And make certain that Billy doesn’t try to take advantage of her in any way.
Our parenting advice is given as suggestions only. We recommend you also consult your healthcare provider, and urge you to contact them immediately if your question is urgent or about a medical condition.