Don't draw too many conclusions from this but low-dose Aspartame affects gut flora in rats and had knock-effects on metabolism which include insulin response.
http://www.ncbi.nlm.nih.gov/pubmed/25313461
Google search terms "aspartame implicated obesity"
The generation brought up on rationing may have splurged on sugary foods when it came off rationing but did they become obese? If not, it may be that the lean times, during rationing, "programmed" their metabolism to behave in such a way that high-carbohydrate intake, in later life, did not lead to making them fat.
There is another strand of research concerning "epigenetics", in which parental metabolism "settings" influence what nutrient levels the foetus is exposed to, affecting its metabolic settings, so factors are "inherited" but this is not attributable to genes.
Synthetic aspartame is, in effect, a change to our environment and the date of its introduction really ought to be marked on any graph of increasing prevalence of obesity (in childhood or otherwise) just so people can evaluate for themselves what the story is; the same way that we know when the industrial revolution kicked off and keep that in mind when looking at graphs of global CO2 concentration and temperature etc.