Height vs growth hormone.

Diabetes (type 2) is primarily a disorder of hyperglycemia. Growth hormone is potently inhibited by hyperglycemia. It follows therefore that height is affected by hyperglycemia through inhibition of growth hormone.

Since growth hormone acts on all tissues, not just bones, it follows therefore that all tissue growth is affected through the same sequence, resulting in smaller organs and skeletal structure overall, which we can see a model of in the Zucker rats (often cited by Taubes in his lectures).

Consequently, we end up with a system that is rendered less able to dispose of excess dietary carbohydrates, except through excess fat accumulation, where fat tissue acts as a glucose sink by virtue of insulin and by virtue of fat tissue's ability to convert glucose to glycerol (and then triglycerides) for storage. And since the liver is now smaller than normal, and since the liver is the primary site of disposal of excess glucose by conversion to glycogen, this allows the excess dietary carbohydrates to cause blood glucose to rise beyond what is otherwise possible in an adult human who would have grown to normal height/size beforehand.

Conversely, while growth hormone is inhibited by hyperglycemia, insulin is stimulated, which then causes fat tissue growth through the process known as insulin-induced lipohypertrophy (or lipodystrophy, depending on your point of view), where fat tissue grows not merely in overall size, but also in number, i.e. there's more fat cells than otherwise.

The combination of these factors then makes possible the observation of an association between height and diabetes (type 2).

Not necessarily how it actually works, just how I see it.