I told my grandparents, and to be honest I'm thankful for their support. They're extremely sweet about it - my grandma is always insisting on attending these little "diabetes education" classes held in back corners of libraries, which I find cute - and my grandfather, a type 2 diabetic, is always cheering me on. Given he's had me beat in the A1c department for the last few months, but. There's something about discussing diabetes with him that makes me smile; it makes me feel closer with him. That, and, he's so stubbornly unfavoring blood sugar testing that he often hands his brand new meters (with strips!) off to me. Which is cool :)
If I was you, of course I would consider telling them. Even if they do worry, you're family. You're their granddaughter. In my opinion, that right there is enough to earn them the right to know. Wouldn't you want to know if something happened to them? Wouldn't you want to know if they were diabetic? Sure, you'd worry. But you'd also want to be there for them.
This is just my opinion. Of course, do what you think is best and what you are most comfortable with. But whatever you choose I wish you the best of luck with it :)