And your question is............??

The plant appears to be a well developed clump of lambs quarters, Chenopodium album, an annual (and also edible) weed. Quite easily removed by pulling.

Thank you, some of them are quite

large and seem deeply rooted (I'll see after I water)

you are correct (don't know about the edible part)

what about these

Those plants grew there and took nutrients from the soil so putting them back into the soil to put those nutrients back simply makes more sense than does pulling them up and tossing them someplace, unless that is a compost pile. Many places today prohibit putting yard waste in sanitary landfills with the thought that this material should be recycled, reused, repurposed on site. But then some places do have ordinances that prohibit composting.

Till them back into the soil or knock them down and cover them with a mulch.

kimmq is kimmsr

In your second picture the plant on the right is Sonchus oleraceus, Sow Thistle. The flowers are already over and the seed head will continue to develop even after the plant is pulled up. Bury it deep in the compost heap. BTW it has a habit of breaking off rather than coming up whole in which case it will regrow. Make sure you get all the root.

If any of your weeds are identified as perennials you need to check their root characteristics before tilling them in. Some love that treatment as it enables them to spread throughout the garden. Every scrap of root can regrow. So keep asking for ids as you go along.

Or, if seeds aren't present yet, pull them up & let them lay there & be the mulch.

The Sonchus has already set seed in the picture. In fact since this conversation has been going a while, if it hasn't been pulled it will have spread its progeny long ago.