It looks like cudweed to me, Mary, which is the favorite host plant for American ladies down here.
Here's a picture -
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And another of the flowers -
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Sherry

Oh, Sherry, I so hope you are correct. It does look like the tiny blooms. Wouldn't that be neat. I will keep the little plants. I do believe your photo looks very much like the plants I found. My back is messed up and I couldn't get down close to the plants to take a proper photograph. Thank you for taking the time to look.

Now I've got to go research Cudweed, as I know nothing about it. Hoping it's a perennial but if not, maybe the dropped seeds will provide more plants next spring. That area is going to be my "Cudweed" bed for the American Ladies BF's!

Ironically, I was pulling up the weeds, thinking I might plant the Pearly Everlastings there. Then I spotted the little plants and the leaves looked very much like the Pearly Everlastings leaves so thought I best leave them and check on their ID.

My thanks once again for your help.

~Mary

It's surprising to see blooms on yours at this time of year, Mary. Down here, cudweed pops up in winter, grows rapidly through early spring, then blooms in mid spring. In summer it goes dormant, with many plants "disappearing" altogether and just a basal rosette of leaves remaining on others.
There are many types of cudweed. The type in the picture is, I think, Gnaphalium pensylvanicum. We also have G. obtusifolium/rabbit tobacco that grows in real dry areas - this type has thin leaves. As long as it's some type of Gnaphalium, the American ladies will (most likely) use it.
It undoubtedly spreads by seeds, but it also spreads from underground roots - I've pulled up the connecting roots.
Sherry

Sherry,

Please look at this ... I think it looks just like the plant you suggested; Gnaphalium pensylvanicum - Pennsylvania everlasting. I discovered this in the weed pile, where I had thrown them. I soaked it overnight in rainwater, then planted and misted it late yesterday. Just look at it this morning! These must be tough little plants. The roots were completely dried out and the plant was extremely limp. I think it's going to survive to become the third plant in my Cudweed patch. :-) I'm going to plant my Pearly Everlasting seedlings in there, too. It sounds like they might become taller than this little guy so they should do well together.

Thanks again for your help.

~Mary

Gnaphalium pensylvanicum - Pennsylvania everlasting

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That's definitely cudweed, Mary, the same type as what grows here, probably G. pensylvanicum. They are VERY tough plants, as you've seen.
Have you ever seen an American lady nest?
Sorry about this picture, it was taken with my last camera, but you can see what to look for -
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American ladies use the fluff in the flowers, plus the seeds, to make their nests, so, since yours are still blooming, there may still be American lady cats on your local cudweed.
Although American ladies don't have a widely recognized migration, like monarchs and painted ladies, I think they do migrate, following the blooming cudweed.
Sherry

Hw sweet is this ... looks a bit like a little hummingbird nest. Now I know what to watch for. Thank you for sharing your photo with us.

~Mary