my two lay medium to large eggs, I think. I don't really know what a large grocery store egg looks like anymore. My EEs (hens about 1 1/2 years old) lay much bigger eggs than my silkies, and bigger than my BO pullets are laying; but not as big as my RIR the same age as they are. Hope this helps.
I have 2 EE;s, one lays a rather small blue/green egg. The other one lays a large olive green egg. They usually lay everyday, but sometimes they take a day off. Right now they are going through their first molt. So no eggs from them at the moment.