Answer: Chickweed (Stellaria) is a cool season annual that reseeds itself and grows in fall and spring. Here are some photos.
To control it you would be sure to prevent it reseeding (pull or spot treat the plants with an herbicide containing glyphosate before they bloom and set seed), avoid disturbing the soil which would bring old seeds to the surface, and use mulch. Applying an organic mulch about three inches thick should smother any seeds on the soil surface and prevent them from germinating.
For insurance, you could top the mulch with a pre-emergent herbicide such as corn gluten. Apply it in late summer and repeat in fall and spring as indicated on the label.
If you use glyphosate, be aware it is a nonselective herbicide and will damage roses if it contacts them. You may find a wipe on application method easier to control than a spray.
Read and follow all of the label directions on any product you use.
I hope this helps!
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