Weed on the left, which we shall nickname Frilly Weed for it's appearance, has really put on a lot of branches. There are actually two of them, one on the left and one on the right. The one on the left now has 6-8 branches emerging from the bottom.
But what is really interesting is how the leaves are filling in. There are now all of these extra branches coming out of the main stalk, just in the last few days.
Here's a closeup of the leaf in case it helps anyone on the ID.
And here is the top of one of the branches.
I have gotten lots of great suggestions, so thanks for your thoughts. Here are some of them:
easter lily mutant gone giant
Have not been able to confirm any of them from looking at images on the web but I'll keep trying and waiting to see what it produces. Feel free to add your$.02 if you have a guess.