But is this fear making children fatter? Possibly. A large study from Imperial College London and the World Health Organisation (WHO) last month found that number of obese children and adolescents (aged 5 to 19) worldwide has risen tenfold in the past four decades. In 2016, the obesity rate was second highest in children in the high-income English-speaking region, (which includes the US, Canada, Australia, New Zealand, Ireland and the United Kingdom). The researchers, who found that four in 10 children aged 5 to 19 are overweight, have warned of an "absolute crisis" in child health including a greater future risk of heart disease, cancer and diabetes.
"The trend predicts a generation of children and adolescents growing up obese," says Majid Ezzati, the Imperial College professor who led the study.
Dr Fiona Bull, from the WHO, says: "We are surrounded by environments that market unhealthy, high-fat, high-sugar, high-calorie food. That's what is on the television, that's what is promoted at bus stops."
But do parents have a responsibility to act, too? Yes, according to Matt Roberts, personal trainer and father of two. "Things have gone too far, and today's parents are fearful of speaking to their child about their weight. But you can do it delicately, appropriately and - rather than singling a child out - you can tackle it as a household."
Roberts says this means leading by example, and being honest about your own eating and exercise habits. "Have a kitchen detox so there aren't biscuits and soft drinks around to tempt them. Don't ban treats entirely, but limit them to outside the house, where you have less control anyway.
"Secondly, get off the sofa yourself. Cycle or dog walk together and make it social by inviting their friends along, too. Encourage them into sports and try different ones until they find something they love."
Roberts says it's no coincidence that childhood obesity rates were lower in 1975. "There were no gadgets or social media to keep them inside and inactive. If your child is under 11, set screen time limits. But if you have a 14-year-old? Good luck with that. I have children myself, so I know it's hard. All we can do as parents is keep trying to engage with them, encourage them into sport and limit junk food at home."
He also advises talking in terms of health and not weight. "Don't tell them they need to lose a specific amount of weight - don't bring numbers into it. Rather, talk about how reducing sugar and getting out in the fresh air will make them feel energised and healthy, how it will make them better at their sport, and so on."
"I often find anxiety about talking to our children about weight is rooted in our own childhoods," says Dr Rachel Andrew, clinical psychologist and author of The Supermum Myth. "I've rarely met a child who is overweight in a family where everyone is a normal weight. Often, one or more parents are overweight or have struggled with their weight in the past.
"These parents often worry about hurting their child's feelings or triggering an eating disorder, but I believe those parents will naturally be more sensitive to their child's feelings so they shouldn't worry."
Dr Andrew says parents should also remember that some children may be more prone to weight gain than others and will therefore need an extra (but discreet) eye on them: "Lots of factors come into a child's weight, other than diet and exercise, like different body shapes, metabolisms and temperaments. Some children respond well to limits. Some children love playing football, whereas others like sedentary things such as art."
And then, of course, there's the inextricable link between food and love.
"As parents, we feel our primary responsibility is to nourish our child. But remember, not gently and kindly tackling a weight issue with them will do them more harm than good."