Diabetes is not (as we thought) the result of being overweight, rather the effect of absence of variation, not losing weight, not having periods of starvation (that among other things, clean up the fat deposit in the pancreas that is Last-In/First-Out (LIFO) (hence path dependent). So someone overweight who loses weight can be much better-off than the same person a bit thinner at stable weight.
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There is plenty of research in diabetes hinting at this from many sides but nobody tried to put a systematic mathematical apparatus on it. Though the math is not trivial (because of path dependence),
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Note that the Russians have known that for over a century.

http://www.ncl.ac.uk/magres/research/diabetes/reversal.htm


See also (easier read)

http://www.dailymail.co.uk/health/article-2385179/I-reversed-diabetes-just-11-days--going-starvation-diet.html