What is the cause when I feel week (as I imagine a diabetic would feel) and break out in a sweat?

Any number of things. You need to see a provider and give a full history. Keep a diary of when this happens and what you have eaten throughout the day.
Hypoglycemia. Just as with a diabetic on medication, weakness, sweating, shaking, anxiety, can be related to low blood sugar. But other sources are possible. Get testing with your physician to find the source.