A Continuous Negative Loop in Her Head

The girls and I were in the minivan talking about bathing suits. This is the time of year when I realize I should have bought the next size swimsuits for the girls. The ones they have won't fit them in a few months. Last year I ended up buying new suits on eBay in January. This year I said I was going to plan ahead.
It turns out that the bathing suits are nearly gone already. I knew this would happen about Fourth of July, but I didn't plan ahead quite like I thought I would.
Plus, we have an additional issue which is that the brunette twin wears a junior or petite women's size now. Have you seen those bathing suits? A strink bikini with a padded top is not going on our third grade daughter.
In the minivan we discussed the possibility of a tankini, basically a two piece bathing suit with a halter top like top and bikini bottom. It wasn't my first choice, but it was a lot better than a string bikini. The girls lobbied hard and I said, "We'll talk to your father about this."
Tears immediately started streaming down the brunette twin's face. She said, "I know why you don't want me to wear a two piece. It's my fat stomach."
After talking to her about why she believed this, I discovered that one of the mean girls in her second grade class kept telling the brunette twin she was fat and ugly. The brunette twin took this mean child's word as the gospel, despite the fact that we talked about how mean and rude and wrong this girl was nearly every night at dinner.
Sigh...
No matter how many times we talk to her, the brunette twin has a loop in her head that says she's not quite pretty or smart or nice enough. I don't know how to change that loop so she feels better about herself. We talk to her constantly about her good points, but she only takes negative comments to heart.
I'm at a loss and she's only eight years old. If this is what she hears when she's eight, what will she hear when she's eighteen?