The study was done in Sweden and involved 4,000 identical twin pairs. The lighter of the twin pairs had average body mass index of 23.9; the heavier twins averaged 25.9. Note that 25.9 is barely into the overweight range.
Type 2 diabetes definitely tends to “run in families.” If you have a genetic predisposition to it, then get overweight or obese, your risk increases even more.
From the abstract:
“In [identical] twin pairs, higher BMI was not associated with an increased risk of MI or death but was associated with the onset of diabetes. These results may suggest that lifestyle interventions to reduce obesity are more effective in decreasing the risk of diabetes than the risk of cardiovascular disease or death.”
PS: Study results may or may not apply to non-Swedes.
PPS: Calculate your body mass index.
Diabetic Mediterranean Diet 