The grass you sent is common Bermuda. Unless you pull it, or kill it with a herbicide, it will likely green up and grow when the weather warms. It likes full sun areas. I think weeds are the result of weakened turf rather than the cause of a weak lawn. So, to control weeds, I try to boost the health of the turfgrass, which in most cases here is St. Augustine.
Good culture is the first step in the control of weeds.
This means proper watering, mowing and fertilizing. Pull weeds when you can, give your turfgrass proper care, and you'll see improvement. Water your lawn when we have not had rain. Grass needs as much as 1 to 2 inches a week to grow. We often get more than this.