No one is immune to cultural imagry Families do not exist in a bubble, outside of culture, immune to its powers. Fathers and mothers are affected by popular cultural images, too.
Parents know what the cultural rules are.
Seeing their daughter put on a few pounds, they may worry about where it will lead, how it will affect her popularity, how this might ultimately make her unhappy and depressed. She'll be discriminated against at work, she won't have a boyfriend. All of these are realistic fears. It's kind of wishful thinking to imagine that things are like they used to be when mom and dad were the most forceful communicators of values. And it's very unlikely that they will be able to monitor their children's activities along these lines 24 hours a day.