I recall an obese patient who was referred to a transplant clinic as his stitch wounds hadn't healed after a year. While there's a myriad of side effects caused by immunosuppressive medication after transplants, the usual healing process for patients that underwent the same procedure is around one to two months1.
It's not an isolated example, as patients with very high BMIs can be considered ineligible for transplantation because of the post-surgical complications that follow, namely, delayed wound healing and increased chance of infection. It does not seem to be dependent on diabetes or merely low metabolism rates caused by a sedentary lifestyle (some of the patients perform well in exercise tests and monitor and control their blood glucose levels) and as such, BMI tends to remain the only (imperfect?) factor.
Why does a large percentage of body fat or a high BMI delay or impair healing?
It seems counter-intuitive to me because, as I understand it, the two major parts of the healing process involve 1) a great range of proteins for the creation of new vessels, tissue etc., and 2) The energy needed for the different processes, such as the mitosis of the cells. If blood glucose levels are close to normal and there isn't much of an insulin resistance, then surely it's not a problem of availability for either of the parts to play their role?
Clarification: I restrict the scope of the examples to transplant surgical procedures as what I state is more likely to be factually correct due to personal experience. I would expect wounds other surgical operations to follow the same patterns, but I could be wrong.
: That is an extreme case, especially considering the possibility of effects of diabetes, obesity and steroids compounding. However, there's a general trend.