Do diabetic complications come from plainly just eating too much or just the sugar itself?

Both: Diabetes does damage when high blood sugar injures cells, & is also associated with high cholesterol and blood pressure (which can be salt-sensitive). Being overweight can increase all of these problems. At any weight, the healthiest diet for a diabetic (or anyone!) is one with lots of natural fiber & fresh natural foods, mostly healthy fats, & minimal processed/refined carbs (sugar, white flour).