One candidate for this plant is Geranium molle, or Doves foot cranesbill. The Inaturalist page gives quite a lot of useful information including distribution and there are many other descriptions of this plant. Arguments in favour are somewhat fleshy stems and leaves, leaf shape, hairy, purplish stems, long petioles. It is highly variable, note the number of varieties.
Sometimes we can get information from the shape of the flowers or fruits. The little balls observed may be either flowers or fruits, take one or two and slice them open to see what is inside; look for layered nascent flower petals or solid fleshy seed. Look carefully and see if any of the balls have the telltale eponymous beak. There is not a lot of root in your photos, is it entirely fibrous root or do the branches spread from a main taproot? Any odour when you crush a leaf?