And around a quarter are overweight when they are just four years old.
Public Health England has released the shocking figures, for which Wolverhampton tops the fat league in the West Midlands.
In the Black Country and Staffordshire, the figures tower above the national averages, particularly for 11-year-olds.
In England, around 33 per cent of children are overweight when they leave primary school, but in the Black Country this rises to around 40 per cent.
Wolverhampton is joint-worst in the West Midlands for fat four-year-olds with 26.4 per cent deemed overweight or obese, the same as in Dudley.
In Walsall this figure is 24.1 per cent and in Sandwell it drops to 21.8 per cent.
All four Black Country areas hover around 40 per cent for overweight 11-year-olds, with Wolverhampton the highest on 41.8 per cent and Dudley the lowest on 38.6 per cent.
In Staffordshire 23.6 four-year-olds are overweight, but their 11-year-old figure is noticeably lower than in the Black Country at 32.8 per cent.
Jane DeVille-Almond (CORR) is a senior health lecturer at the University of Wolverhampton and also chairs the British Obesity Society.
She said it was no surprise that the Black Country was above the national average in the obesity league and that the figures reflected an ongoing trend.
"As with any industrialised community where people historically eat foods with a high percentage of fat it's difficult for people to change their dietary habits," she said.
"There's a clear link between poverty and deprivation - it's nothing new.
"In Wolverhampton it would be wonderful to show we can turn it around - we need to show the rest of the country we can do it.
"We need to tug at the heartstrings of parents.
"We've got a generation of kids who haven't watched their parents cook meals or families sit down to eat together.
"That needs to change."
Health bosses in Wolverhampton last year made tackling the city's obesity crisis their top priority.
Public Health England released the child obesity figures as it launched its Change4Life campaign to encourage parents to cut down on the amount of sugar their children eat or drink.
Professor Kevin Fenton, national director of health and wellbeing at Public Health England, said: "Reducing sugar intake is important for the health of our children both now and in the future.
"We are all eating too much sugar and the impact this has on our health is evident.
"This campaign is about taking small steps to address this."