Congratulations on the new great-granddaughter. I dislike the name, but I'm sure the little girl is darling regardless of what her name is.
The meaning "delicate, weak, languishing" is not empowering. Since the name is so associated with a particular character, it even has a dictionary definition.
Delilahnoun
1.
Samson's mistress, who betrayed him to the Philistines. Judges 16.
2. a seductive and treacherous woman.