In diabetics, the excess may be transferred to the developing infant, which grows too much as a result and is then itself at higher risk of the condition when it becomes an adult.
All this is a reminder of the delicate balance between mother and child; not, as many parents imagine, one restricted to adolescent tantrums but one that begins at the moment of conception and persists through life, and even into later generations.
When, long ago, I was a student in Edinburgh, I was taught by some of the great figures in genetics (of course, I did not realise that at the time).
One such was C.H. Waddington, who gave us baffling lectures on what he called "epigenetics", a word he had coined.
It had, as far as we could work out, something to do with the mysterious landscape that lies between nature and nurture; with the ability of the environment to influence the action of genes.
The cynics among us felt, perhaps rightly, that it really meant "we have no idea what is happening, so we will solve the problem by naming it" - but now, at last, we have some idea.
Obesity plays a large part in the story.
Worldwide, 21 million children under 5 are overweight.
Once, their condition was blamed on mere weakness of will or on "glands", but the problem goes much deeper.
Whatever lies behind it, obesity comes from an increase in the numbers of fat cells, or adipocytes, and is hence due to a shift in the activity of certain genes during development.
The details are complicated, with a battery of mechanisms that switch sections of the genome - and even whole chromosomes - on and off, suppress potentially harmful parts altogether, and persuade them to increase or decrease their activity.
Some of these epigenetic marks last just a few hours, while others persist for a lifetime.
They can be sparked by a great variety of agents - over-eating, a high-fat diet, inactivity, a side-effect of certain drugs, or depression - that reduce the brain activity interpreted as pleasure (from a good meal included) and increase the amount of food needed to be satisfied.
Poor sleep, and even working night shifts, also increase the chances of obesity, and childhood stress of various kinds, and problems with sexual development may be involved too.
For obesity and for many other things, there is a link emerging between body and mind; between being overweight when young and adult depression, anxiety, autism, memory loss and more.
These links may seem baffling, but they come from the ability of childhood obesity to shift the settings of a whole range of genes.
In the brains of the very overweight, whole sections of DNA seem to escape from epigenetic control, as further evidence of a shift that goes far deeper than the fat cells themselves.
The placenta itself produces nerve transmitters, together with hormones that alter both appetite and mood; and stress hormones from the mother may also leak across it.
Together, they lead to an increase in the numbers of cells in parts of the grey matter associated with appetite, and to shifts in other sections associated with learning ability and mood and - in mice at least - in those involved in social interactions and liability to addiction.
As many people know too well, excess weight is hard to shed; and even if a crash diet works for a while, the pounds tend to creep back on.
Epigenetics is at work.
Once its controls have been set by the onset of obesity, before birth or later, it is very hard to turn the molecular machinery back to a time before it was first tuned.
The genes retain a memory of the environment they faced long ago, even if the fat itself has been cast off.
As the record-breaking German baby shows, that can persist from one generation to the next and - we now know - even into the second and third; and even when fathers, rather than mothers, are too fat.
Waddington's new word now haunts his science and reminds us that genetics has a lot of weight to lose before it can return to the elegant simplicity of my student days.
Tipping the scales
• In July, Addyson Gale Cessna was born at 6.24kg at Armstrong County Memorial Hospital in Kittanning, Pennsylvania.
• In March, an even bigger baby in Britain, George King, came into this world at a whopping 7kg.
• In July 2011, Texas baby JaMichael Brown, nicknamed Moose, was born at an impressive 7.28kg (16 lb 1oz),
• 21 million children under 5 are obese.
