(I'm sure the Blue Prince and baby H both already known all about this; they're the experts on this topic, not I!)
The word mellitus is the latin word for "sweet as honey" (also the French word for honey is miel). Honey pee is what doctors used to describe the urine of a diabetic patient. When the body has too much sugar and is in a state of hyperglycemia, the kidneys stop filtering out glucose and let the extra sugar be secreted into the urine. This makes the urine sugary. Back before labs were readily available, doctors used to taste the pee of a patient they suspected had diabetes, and if it tasted sweet, there hypothesis was deemed correct. Aren't I glad that I can now order glucose-tolerance tests from laboratories instead of tasting my patients' urine if I suspect diabetes :P
Image source here.