How often do you water and for how long? How high/low do you mow? The weeds can be handled by something like Spectracide with Atrazine. But I would wait until the grass returns. I have gotten excellent results for fungal disease using ordinary corn meal. It is an organic approach that the experts at Texas A&M swear up and down does not work, but it has worked for me every year since 2002. It is a complete cure in 3 weeks. I am suggesting you try that because corn meal doubles as an organic fertilizer. Your spots don't look that much like a disease, but it could be. If you did not have the really healthy stand of grass right by the sidewalk, it would look more like disease. I would hit it with corn meal at 20 pounds per 1,000 square feet now and again in 3 weeks. If you don't see new grass coming up in 4 weeks, then get a commercial fungicide that works in your heat/precipitation zone - read the label closely to see how to apply and when. Corn meal has no restrictions on how or when. Then once you get the grass growing, zap the dollar weed (I assume dichondra or some other easy weed) and let it grow. And if you have not already raised your mower to the highest setting, do that yesterday.

For newcomers this site is actually pretty hard to navigate, edit, post and upload pictures. But since we are on the topic of Velvet Leaf and in light of the toilet paper madness because of covid19, I just gotta say.... If we ever DO have to worry about toilet paper shortages... (which is NOT at this time btw) I would just forage around for this plant! The leaves make an acceptable wipe (or so I heard).

Looks similar to Microstegium vimineum, Japanese Stilt grass. Here is a link that might be useful: Japanese Stilt Grass

It looks like Poa Trivialis ( roughstalk bluegrass) . Its used to winter-seed bermudagrass putting greens in the south, or in shady areas in the north. There is no selective control. You pretty much have to kill the patches with 'Round up' , and re-seed or use sod for a quicker fix. In the future use a weed preventer ( pre emergent herbicide) in the spring.