I'm not sure what it is. Maybe you can find the answer here:Weeds

Here is a link that might be useful: Weeds

Can't see details very well. But might be very leggy chickweed.

Beyond that, the grass is a tad sparse to be called a lawn.

What do you mean? I moved in about 7 months ago, new to the lawn game - Do I need to keep seeding and overseeding? the lawn seems pretty extensive to me...

Look at your pictures. You can see soil between the plants. You seeds should be filling in the spots. Questions to ask yourself. Are you getting the seed from the same supplier, maybe you should try a different brand. Are you watering every day when you sow the seeds? Have you put a light covering on the spots that you are reseeding such as bagged compost or topsoil. This will help keep seed from washing away.

Check the lawn forum for other suggestions.

Difficult to say but that could be Black Medic, Chickweed, or about any other creeping plant we consider a "weed". The single best way to prevent "weed" growth in turf is to grow a good strong turf that keeps "weeds" from getting a toe hold and the starting point there is a good, reliable soil test. Many "weeds" grow in soils not really conducive to good turf grass growth so contact you local office of the University of Gerorgia USDA Cooperative Extension Service, http://www.caes.uga.edu/extension/statewide.cfm about having a soil test done.

Here is a link that might be useful: Weed Alert

Re your lawn, if you want to keep the birds from eating all the seeds off it (as they LOVE to do), spread some straw over the seeds you put down. Just make sure it's straw and not hay, or else you may get hay in your lawn too.