I don't know about the waffle iron and not much more about the star marking. The star marking shows up every now and then. I believe they are bean pots. At least that is the only ones I have seen. I believe that they come in only one size but again I am not certain of this. No one knows who made them or when. Some of the cast iron, without some kind of documentation, we will never know who made. But I do have a cover to one. Does your cover look like this?
And could you post a picture of your waffle iron? With a picture maybe we could come up with a answer for you on that one.