hey fata ... back in the day.. in suburbia... on a 50 by 100 foot lot.. i too dug things out ... today on 5 acres.. i am a one man crew ... i have no other option ... and i do note.. you actually use it for a purpose... it has no purpose in my yard ... and anything that has no purpose.. is commonly called.. a weed ... i am agreeing with you when you said: There are different lines of gardening thought not arguing, nor being defensive ... ken

Looks quite like Houttuynia cordata, which also has a strong scent when crushed. Goes nuts around very moist areas and becomes invasive. hortster

Could be "Mallow neglecta" a fairly common lawn "weed" sometimes misidentified as ground ivy. The "weed killers" probably killed off the plants that were there but new ones appeared from the prolific seeds these things produce. Perhaps this article might be of some help. http://www.better-lawn-care.com/common-mallow.html#axzz4mEYDCWro

I guess down here, where the stalk doesn't sometimes die back in the winter, it might seem like a perennial, but Amaranth is really an annual. I've never seen it come back from the roots, but I've seen another plant sprout up right next to where last year's was, so it may seem like it does. Pusley has a long, deep root that is hell to dig out if you get a mature plant. They also seed like crazy.