Among the echoes of basketballs bouncing and sneakers squeaking on the gym floor, Averill often would hear girls who she thought were her friends singing a jingle. Their carols were often directed at her.

"Wonder blob," their shrill adolescent voices sang aloud.

Averill's cheeks would turn crimson and her palms clammy. In that gym, at a private school in upstate New York's Westchester County, is where Averill said she felt the most excluded. The gym teacher would do nothing, she said.

Lindsey Averill, around 16. Her supportive family helped her cope with bullying, she says.

"I definitely got bullied by people who I cared about and I definitely had people I thought were my friends that weren't," said Averill, now 39, as she reflected on her middle school friendships. She added that her weight was often the target of the teasing.

Averill and the girl who dubbed her "wonder blob" are close friends today, Averill said. They reached an understanding and have grown closer in their friendship. Yet those many years ago, the girl fit the definition of a "frenemy."

"Kids can be mean. We have to accept that that's part of being kids, but I do think that fat kids are specifically targets," Averill said. "Overweight kids particularly are susceptible to (frenemies) because they are already in positions where they feel like they have to fight to belong, so they are more likely to accept the treatment of a friend who puts them down."

Lindsey Averill, around 4 years old, playing in a tire swing.

Two separate studies published in June support Averill's idea that overweight or obese children are more likely to have "frenemies" than non-overweight children.

"What we consistently see across time is this unreciprocation of friendships, so overweight kids not having their friendships reciprocated, especially by non-overweight kids. So, that's something, in a number of studies over time and across countries, that we've seen," said Kayla de la Haye, a behavioral scientist and assistant professor at the University of Southern California who was lead author of one of the studies, published in the journal Plos One

"We might expect that as rates of obesity go up and it becomes more normal or common, that we would see people sort of accepting that as a characteristic more," she said. "What's probably surprising is how consistently we see this rejection and how strong the effects are for overweight kids being disliked by their peers just really based on that characteristic."

The percentage of children with obesity in the United States has more than tripled since the 1970s, with about one in five school-age children being obese, according to the US Centers for Disease Control and Prevention . Similarly, in the United Kingdom, about one in five children age 10 to 11 are obese, according to the country's National Health Service

Frenemies and weight-related bullying can have a negative impact not only on overweight children's emotional health but on physical health, and it could lead to more weight gain for a child, de la Haye said.

Obesity during childhood is associated with having a higher risk of high blood pressure, high cholesterol, type 2 diabetes, breathing problems, and bullying and stigma, according to the CDC.

Why overweight children are more likely to have 'frenemies'

For the new Plos One study, de la Haye and her colleagues analyzed data on 504 children from 28 separate primary education classrooms in the Netherlands. The data, collected between 2001 and 2002, came from an ongoing nationwide research project called the Tracking Adolescents' Individual Lives Survey

The data included questionnaire responses in which the children indicated who their best friends were in the classroom as well as the classmates they disliked in their class. The height and weight of each child were also included in the data and used to calculate each child's body mass index.

The researchers found that overweight children not only were less likely overall to be nominated as a friend than their non-overweight classmates, they were 1.65 times more likely to be disliked.

"We see examples of where there's overweight kids who will say 'Yeah, this person is my friend,' and that person has actually said, 'No, I actually dislike (the overweight kid),' " de la Haye said.

"This negative social environment is important to address because it can have a negative impact on overweight children's mental health and because it is a barrier to overweight kids adopting healthy habits," she said, adding that stigmatizing obesity does not motivate children to lose weight. "Overweight kids who experience peer rejection and social isolation are likely to exercise less, have greater food intake and have fewer positive role models for healthy habits and a healthy weight."

The new study had limitations, since it involved a sample of only Dutch children and examined friendships within a classroom and not outside of a school setting.

"This is really the first study that's looked at the 'dislike' relationships with that," de la Haye said. "We need to do a little more work to see if this would generalize to kids in the US; what we expect is that it would. ... Weight-based stigma seems to be something that's very common across countries."

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Dr. Eliana Perrin, senior author of a separate study published last month in the journal Pediatrics , said children might carry an implicit bias toward their overweight peers, which could lead to unreciprocated friendships and bullying.

"Implicit bias probably does explain part of why children with obesity are more likely to be bullied," said Perrin, chief of the division of primary care in the department of pediatrics at Duke University School of Medicine.

"But it's important to realize that some children also have explicit bias and are conscious of the fact that they'd prefer a friend who is thin or would actively exclude a child with obesity from a sports team," she said.

'It's something that's learned pretty early'

The new Pediatrics study involved 114 children, 9 to 11 years old, in the Chapel Hill, North Carolina, area. The children were shown images of other children, of various weight sizes, for 350 milliseconds. Then they were shown a meaningless fractal image for 200 milliseconds and were asked to rate the abstract fractal image as "good" or "bad."

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The researchers designed the study using the Affect Misattribution Procedure , a method known to measure implicit attitudes.

The researchers found that, on average, 64% of the fractal images that followed an image of a healthy weight child were rated as "good," compared with 59% of the fractal images that followed an image of an overweight child. The finding suggests a weight bias of 5.4%, according to the researchers.

"We were surprised that the degree of weight bias was this significant, even in this young of a group," Perrin said.

Most of the children in the study, 69%, were white, and more research is needed to determine whether there are differences in bias among a more nationally representative population, Perrin said.

As another example of weight bias, de la Haye, who was not involved in the new Pediatrics study, pointed to a previous study on the stigmatization of obese children. That study also had a majority, 71%, of white participants.

The study, published in the journal Obesity in 2003, involved 458 fifth- and sixth-graders who were asked to rank six silhouettes of children in the order of how well they liked each child in the silhouette drawing.

The black-and-white silhouette drawings appeared in a variety of sizes, ranging from skinny to obese, said de la Haye, who was not involved in that study.

"Just based on that, kids would say, 'I prefer to be friends with the skinnier stick figure,' " de la Haye said. "It's something that's learned pretty early as this important marker of a characteristic that we dislike in people and that translates to social behaviors like rejection and bullying."

Averill, who was once bullied for her weight as a child, said she hopes to eliminate this weight bias seen among children.

How you can stop weight stigma

Averill and her business partner, Viridiana Lieberman, produced a documentary titled " Fattitude " that sheds light on how popular culture can foster weight biases.

The film premiered in May at the DOXA Documentary Film Festival in Vancouver, and it is scheduled to be screened in November in New York to benefit the Binge Eating Disorder Association , Averill said.

Lindsey Averill, now 39, and her business partner, Viridiana Lieberman, while filming their documentary "Fattitude."

In most films or TV shows, "if I'm living in a fat body, I'm the fool or the monster, like Ursula the sea witch or the Penguin from Batman or Jabba the Hutt, who is literally a mound of fat," Averill said.

"If I'm a fat female in films, I'm either very hypersexual, where I'm like throwing myself at a man -- we see that a lot with Rebel Wilson. Or, I'm the opposite; I'm completely and totally neutered and asexual and never thought of as having a sexuality at all. We see that a lot with mammy or mother figures, where there's just a large women who everybody thinks of as providing food and care with no concern for her own needs," she said. "These kinds of messages bleed into our cultural thinking, so we then take those stereotypes and lay them over the people we know in the real world."

Sometimes parents may be unknowingly passing judgments about weight down to their children, Averill said.

"We may be looking at our children and saying, 'You are beautiful; you are perfect,' but every time we look in the mirror, we're saying, but 'I'm so fat, and I'm so ugly,' so that we're passing along that message without actually directing it towards our child," she said. "We're passing along that message that, if our child is thin, then fat people in fact are worthless. So culturally, we need to shift gears."

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Now that weight stigma has been identified, Perrin, the researcher at Duke University, said there are several ways you can address the stigma, especially among children.

"One is to encourage kids to actively think about and combat weight stigma. Even though they have implicit biases, they can work to avoid acting on those biases," Perrin said.

"The second is to educate kids in media literacy so when they watch movies, see advertisements, engage in social media and so on, they can recognize and guard against stigmatizing messages," she said. "A third is to work with media, parents, schools and doctors to combat the stigmatizing messages and replace or supplement them with positive messages that have more to do with how people act, rather than how they look. We have reason to believe that all of these have the potential to help."