The second weed might be Japanese Stilt grass, Microstegium.
Removing the plants before they set seed will greatly reduce next year's population. Look to remove all of these by mid-August or so.

Here is a link that might be useful: Japanese Stilt grass

A good pre-emergent works well on Microstegium. You need to get it down by the first of the year. And, if you put it down NOW, you can probably eliminate some of the other annual weeds.

I was told burning when the Microstegium is just coming up also works. I plan to try that this year down at the lake since I don't use chemicals near the water.

I've never been able to completely win the war with these two trouble makers. I can knock them back with hand pulling throughout the year but they always come back the next year. At least they are easy to pull and easy to spot in the flower beds.

maybe once the kudzu beetles finish off the kudzu they will turn their attention to stilt grass.typing one-handed with a pbj sandwich in the other

Put down the sandwich Dottie - those guys have already discovered how good Soybeans taste. I imagine they'll figure out Lablab or Hyacinth Bean before too long.