Why do obese people heal more slowly?
It's well known that obese patients have slower wound healing, but the specific cause isn't known; most likely there are multiple causes acting together. 


  The correlation between obesity and deficient wound healing has long been established. ... Substantial evidence exists demonstrating that obesity is associated with a number of postoperative complications. Specifically in relation to wound healing, explanations include inherent anatomic features of adipose tissue, vascular insufficiencies, cellular and composition modifications, oxidative stress, alterations in immune mediators, and nutritional deficiencies. 


--Obesity and Surgical Wound Healing: A Current Review  (This is an open-access article that nicely summarizes the open questions)


  Obesity has been shown in a number of studies to impair wound healing, and chronic nonhealing wounds in obesity and diabetes are a major cause of limb amputations in the United States. ... Recent evidence indicates that aberrant wound site inflammation may be an underlying cause for delayed healing. Obesity, diabetes, and other conditions such as stress and aging can result in a chronic low-level inflammatory state, thereby potentially affecting wound healing negatively.


--Exercise, Obesity, and Cutaneous Wound Healing: Evidence from Rodent and Human Studies (Also open-access, a little more recent but less wide-ranging)