They also have a heightened chance of long-term health problems, with around 16 per cent of pregnant women in the Lothians understood to be obese.
And with around 10,000 newborns a year in the area, it means a significant chunk of them will be disadvantaged.
The warning comes from baby charity Tommy’s, which works extensively in the Capital.
Experts who carried out the research with the organisation added there was low awareness across Scotland about vital pregnancy issues.
That includes ignorance about calorie intake in new mothers, the risks of over eating and the importance of vitamin substitutes.
Health campaigns director for Tommy’s, Jacqui Clinton, said: “Poor diet, obesity, lack of physical activity, smoking and mental health problems can all impact on the healthy development of the baby.
“However, we know changing behaviour and certain habits can be hard.”