That is another member of the nightshade family; the tree seedling looks like a mulberry.Is the root bright yellow?

The first one is black nightshade, Solanum nigrum or a very similar species. The second is a mulberry seedling.

Thanks Lisanti and Denninmi! Nice, another nightshade :) I remember seeing the purple flowers one before but this is new.
So it is mulberry. Hmm, I don't even remember seeing any mulberry trees around here. If I think of the same tree - short with dark and white berries which kind of resembles elongated raspberries and dark ones leave stains :) I kinda like the fruits.

I don't know about the root, this particular one is in the neighbors yard. All these weeds pics are from their yard (not that I am free of them, but theirs are bigger ;)) That's another problem, how to tell them. They are new neighbors and I used to help the previous neighbors with weeding sometimes. Then the left side neighbors have a field of creeping charlies and all those weeds want to get into my yard! :))

Anyway, thanks again, people are very helpful here! I have another weedy ground cover which we are trying to id for years, I go to nurseries every year and look at all their ground covers because that's where my husband bought it, no luck so far. I'll take a pic and try here ;)