Please settle a debate. Which came first; big babies or diabetes? My understanding was that having large babies was a sign of blood glucose issues.

Correct. Babys born to a mother with diabetes including gestational diabetes are heavy. In addition, they often develop low glucose after birth.
What debate ?? Diabetes of pregnancy(gd) is a common pbm & signal that a woman will likely have adult onset diabetes in later life, but pregnancy brings it out, at least for the pregnancy. Babies make their own Insulin during pregnancy, so any poor control mom has is reflected in extra baby size & weight & possible need for IV fluids at birth. Mom's gd doesn't translate to a fat toddler or child , just a big start.
Possibly. Some large or above average weight babies can be due to gestational or pregnancy related diabetes. But often it may not be related to that at all. It really depends on mom's pregnancy history and what baby presents with after birth. Check with your primary doctor or ob/gyn to be sure.