If you used that dinnerware every day, you've received about as much radiation from the dinnerware as you have from the potassium in your body (about 400µSv/year).
You'd need about 100,000 µSv/year to get heightened cancer risks.
Upthread people are saying is not recommended. Not because of the radiation when eating off it, but if there's any chips or anything you should end up with uranium inside of you, which is significantly worse.
But as long as it's intact, no big deal. (I guess, I'm not an expert, why are you listening to me?)
I inherited them from my grandmother. Should I be worried about having used them for years?