No, It need not have anything to do with sin at all.
Eve was created without sin. Do you doubt that?
No I do not doubt that.
Wouldn't being created without sin be a greater thing than being created with the stain of sin? (Original sin, we speak of here.)
Perhaps, though beside the point.
That means Eve would be more blessed than Mary, unless Mary was also preserved from Original Sin.
Not at all. Being chosen to be the vessel which brings the Living God among men is a higher honor than any, and that is the point of "blessed among women", not her condition of sin, one way or the other, but in spite of it.
LOL. OK, thanks for playing.
So far today I've learned that unity with God in Heaven is not something to aspire to and that one can be full of sin and still be more blessed than any other woman, even one created without sin.
Oh, and that the admonition about the "unlearned" getting confused on hard parts of Scripture is nothing to worry about.
The phrase for “blessed” used of Mary is also used of Job in James 5:11. For his endurance. As you suggest, being blessed does not necessarily have anything to do with sin, but with being used by God.