From the first picture I thought Penstemon, but not from the second, sorry!

reminds me of gypsophilia and annual night phox. Do you have a bird feeder that could have spilt seed? What did you grow in the pots last years? I'd be tempted to leave it and see what comes from them.

No bird feeder nearby, they are all round the other side of the house. We did try to grow some gyp last year but without success. The pots contained a variety of things last year....

perhaps it is the gyp from last year did you sow it as seed?

It was sown as seed but not in any of those particular pots I think. Like with the layered bulbs, I guess we just have to wait and see! Thanks for the responses -at least no one has immediately identified it as a tricky weed!

Things that come up all over the place are always weeds in my garden!

Further discussion with daughter produces the information that "I might have scattered the gyp seeds amongst many pots..." So that's probably the answer and we continue to wait. Certainly nothing appeared last year at all.