Being overweight decreases insulin sensitivity for all diabetics. The added weight makes the tissue receptors either non-responsive or less responsive. The lack of a normal "sensing" response means the working endocrine pancreas is dealing with a higher than normal demand to produce insulin; this can exhaust or "burn out" the islet cells. 
Losing the excess means some help with increasing insulin sensitivity. Weight loss usually brings a decrease in insulin needs with it. 
Abstract #68  from the American College of Veterinary Internal Medicine-2004, equates improved blood glucose control with increased insulin sensitivity.
Until this time, insulin sensitivity had not been studied in dogs who had naturally-occurring diabetes. It proved that dogs whose glucose control improved, became more insulin-sensitive and may require less insulin to avoid hypoglycemia.
It is certainly possible to be more sensitive to one species of insulin than to others and also to be more sensitive to a type of insulin in that species than to others. Personal experience with pork insulin proved a much greater sensitivity to pork insulin in Lente form than to pork NPH insulin.
Lack of insulin sensitivity is also known as insulin resistance. There can be more than one reason for this lack of sensitivity, or resistance.
- ↑ Vetsulin-Insulin Resistance-Stress,Infections & Obesity. Intervet.
- ↑ Vetsulin-Stress, Infections & Obesity (Page 20). Intervet.
- ↑ Insulin control. Intervet.
- ↑ Abstract #68-Improved Glucose Control Means Greater Insulin Sensitivity in Dogs-page 26. ACVIM (2004).