Lisa, you don't mention anything about the leaves.* Do they appear normal?* I'm not finding anything with what you are describing.* This site has some good pics and descriptive info, but no match to what you describe.*
I wonder if it could be the intense heat and/or drought or possibly a late infection of phytophthora blight.* The symptoms of this blight show differently depending upon when the infection occurs.
Maybe bacterial soft rot?
If the rot starts at the end of the fruit not attached to the plant, that would be blossom end rot.
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.