Hi , I believe your weed is called Prostrate Knotweed (Polygonum aviculare) which is a low-growing annual; it germinates early in the spring. This weed is usually found in areas where the soil is hard and compacted. Relieving soil compaction by aerating will help to eliminate the growing conditions for this weed.
If you spray to control this annual, do so early in the spring just after you notice it coming up and use a typical lawn weed spray that contains 24D. Try to time your spraying for when the air temperature is between 50 - 80 degrees F. and there is no rain forecast for 24 - 48 hours.