look out for

Idiom: look out for somebody／something

1. to feel responsibility for someone or something; watch out for somebody/something
e.g. I have a network of neighbors who look out for each other and support each other.
2. to be aware of the existence of someone or something
e.g. Everybody thought I'd win, but I kept telling them to look out for Walter, too.
e.g. Look out for the extremely vulgar language in the middle of the movie.

So in your sentence, “look out for” means “look after” or “take care of”，即「照顧」；「為她付責任」之意。

In this sentence, it means
to think only of somebody's advantage;只考慮某人的利益/處處為某人着想
to make sure that someone is well-treated 關顧某人