With the late blight the spots on the leaves initially appear as water soaked spots.* Notice any of that?
I've not heard of more then one spot on the blossom end rot and it only effects the fruit, not the leaves.
Bacterial spot usually has more damaged spots on the fruit.
Buckeye rot is another to look at.
Also look at phoma rot.
This Florida site has more ideas.
When weeding, the best way to make sure you are removing a weed and not a valuable plant is to pull on it. If it comes out of the ground easily, it is a valuable plant.