Could your vine with tiny white flowers be chickweed? Here is a Q&A courtesy of
www.carrollgardens.com newsletter:
Question: Here are some samples of the weeds in my lawn. Is there a way to kill them without killing the earthworms of which I have an excellent population? Without killing the grass I do have left? I live in Glen Rock, PA and I have to be careful what I use as my yard is sloped and runoff will travel to plants I want to live.
Answer: With modern weed killers, especially liquids applied according to label directions, you need not worry about the earthworms or runoff. These weed killers work through the leaves and you need only a tiny amount of active ingredient for them to be effective. Once the weed killer dries on the leaves, it essentially stays there and does not wash into the soil.
The weed that you have identified as the worst (the one with the very small light green leaves and tiny white flowers) is chickweed. It germinates from seed in the fall. Chickweed grows larger and blooms over the winter, especially during mild periods, drops its seeds and then dies in the summer heat. In this year's mild winter, chickweed has grown prolifically and seems to be smothering out everything in its path. Winter application of weed killers is usually not effective because even winter weeds are not growing actively enough in winter. If the weather stays unusually mild so that the winter weeds keep growing quite vigorously, Bonide's Weed Beater Ultra may be effective this winter.
In any event, as soon as the weather warms in the spring, spray all of the weedy sections of your lawn with Weed Beater Ultra lawn weed killer - even if you sprayed this winter.
To prevent winter lawn weeds next year (prevention is the most effective control), apply a weed preventer in mid-September. This will kill the weed seeds as they germinate. The best of these weed preventers is Portrait. Dimension Crabgrass Preventer also suppresses many winter weeds, although not as effectively as Portrait. It can be used as an alternate and applied at the same time.