Problem with yard soil and grass
Judging from your photos it appears as if the soil there might not be quite right to grow good turf grass. The soil appears rather compacted and lacking in organic material. Weeds aren't as fussy as grass and they grow where grass can't.
I don't know what type of grass you are trying to grow, but I think you should start by trying to improve the quality of the soil. You can do that by first understanding what the texture and the chemical content of your soil is. You can pick up a soil test box and instructions from your local cooperative extension (for you I think that is in Montross). The box itself and instructions are free, but you will need to mail it to our Virginia Tech Soil Test Labs yourself (with a $10 check) for a soil test report. The report will tell you specifically what you'll need to do to amend the soil so that it is more suitable for the type of turf grass you decide to try to plant this fall (cool season grasses) or next spring (warm or cold season grasses).
Tilling the area and adding generous amounts of organic matter (compost and or loam) is something that you will need to do sometime this season before you plant any more grass seed. Now probably wouldn't be a good time to do that unless you are willing to grow some sort of cover crop (clover, alfalfa, buckwheat for example) to help keep the soil aerated, fertile, and free from (or low in) weeds.
Because we are well into spring now, it may be too late for you to do any reseeding with grass seed (cold and warm season grasses) now, but you can take steps to improve/amend your soil in preparation for the next time you seed your lawn.
The "powdery soil puffs" in your photo appear to be ant hills (or the hills of some other species of insect). In order to know the species of ant (or other insect), you may want to dig down a few inches around one or two of the mounds and see if you can capture some of those insects that can then be separated from the soil and then put in a vial filled with alcohol. You can bring that vial to your local Cooperative Extension office for them to have it sent of examination by Virginia Tech. That particular service is free. You can call your local Cooperative Extension (Montross, VA) at 804-493-8924 for more assistance on how to get your samples to the Virginia Tech Lab.
I am attaching a few VT Publications on Establishing Lawns, Lawn Fertilization in Virginia, and Turfgrass Varieties recommended by Virginia Tech for the 2018-2019 season.
Have a Great Gardening Day,