I have this ground weed that I cannot control! It looks like a type of ivy. Its roots are white and they go all over and then down deep so I can never get them. I can pull the tops and within one week the ground is covered again. It is in my flowerbed. So frustrated!
I cannot tell exactly what the weed is from your picture, but it may be a type of morning glory weed. I suspect that even though you are pulling it out, small parts of the root systems are breaking off and capable of starting new plants in the soil. I see that you do have your gardens mulched and mulching sometimes helps to keep weeds under control. You might want to try a type of fabric mulch next year, that is placed in the flower bed before you plant annual flowers. You can then plant into holes in the fabric mulch and also can place shredded bark mulch over it to have the look you have had.
Some of these weeds are very prolific in the spring and early summer and may not be as much of a problem in the late summer when the flowers grow taller and shade them out.
If you would like it identified more completely, please submit a sample to your local Cooperative Extension Office on Wyoming Rd in Newark. Thank you for contacting Cooperative Extension,