be somebody's baby

be (one's) baby

1. To be a project or goal that one has initiated and is very devoted to realizing. That initiative is Cheryl's baby, so you know she's going to do everything she can to make it successful.
2. To be one's cherished possession. That car is Mike's baby. If it gets a scratch, he'll be inconsolable.
See also: baby

be somebody’s ˈbaby

(informal) be something that somebody has created, is dealing with, etc: Mary’s the lawyer, so the legal problem’s her baby.
See also: baby