Katherine Schwarzenegger, 20, the oldest child of California Gov. Arnold Schwarzenegger and journalist Maria Shriver, has penned a new book, scheduled for release Tuesday, about how she and other young women deal with body-image issues. Something that's key for girls trying to gain perspective these sensitive matters, she argues, is sustaining a close relationship with their mothers. "My mom was always good with me. She always checked in with me. I had the best relationship with my mom. I still do. I talk to her four times a day," Schwarzenegger tells USA Today. She also notes that both of her famous parents tried to shield her and her siblings -- Christina, 19; Patrick, 17 this month; and Christopher, 13 this month -- from the harsh glare of the Southern California celebrity-publicity complex. Her parents "were very protective of having us in the public eye when we were younger," she tells the paper. "We didn't go to Hollywood premieres. We practiced community service. We went to school and camp like normal kids." [Related: California workers boycott movie over Arnold's cameo] Still, even with a protective set of parents, Katherine Schwarzenegger -- who is now a junior at the University of Southern California -- says she became "self-conscious" about her weight in her middle-school years. She tried to ward off such feelings by undertaking an informal contest with a friend who was naturally thinner to keep their weights beneath 100 pounds. (Schwarzenegger is now 5-foot-8 and a size 6, the paper says.) But weight loss didn't become the obsession for her that it did for many girls, she says. "I did not have an eating disorder at all," she says. "It was like a friendly competition."