I am having a hard time making out what weed it is from the picture. Bringing it in to your local extension Office would help confirm the weed.
However, if it is spreading by putting out runners, as it appears to be doing from the picture, it is most likely Bermuda.
You can also pull some of the weed and place it on a white sheet of paper and resubmit your question. This would help me confirm what it is as well.
If it is Bermuda, there is no selective control available. Spot spray with Roundup and reseed ingredients the area is your best option.
Your weed appears to be large crabgrass. It is an annual that germinates in late April or early May and will continue to grow until the first frost in October. You should treat the area next spring with a pre-emergent herbicide before April 15. This fall I would try to pull out as much as I could and reseed the area with a good lawn type tall fescue such as falcon 3. Anyplace the grass thins will be susceptible to crabgrass infiltration. You can do a search for university of Kentucky publication AGR 78 for a list of chemicals available for crabgrass.