Retired English Teacher
Must be a BrE. v. AmE. thing.
Thank you everyone for giving me your ideas.
Well, here's my conclusion.
Take after is casual language which often shows more regional variation than more formal language. Here's an entry from a dictionary:
to be like (someone, especially a parent or relation) in appearance or character
Example: She takes after her father.
And some examples:
“He takes after his father. All the men in his family are big.”
"Jenny takes after her grandfather. They’re both really good with numbers."