Symptoms are referred to as "clinical signs" or "signs" in animals. High blood glucose concentrations produce the signs of diabetes mellitus.
The "glucose threshold" of the kidneys can be exceeded due to excessive glucose in the blood resulting in the excretion of glucose in the urine. Your dog's increased rate of urination results in extra bodily fluid loss and causes your diabetic dog to drink more.
A diabetic animal may suffer weight loss despite eating more than normal due to the loss of glucose, an important fuel (energy source).
See Diabetes mellitus in dogs for further information on glucose metabolism.