I'm not an expert by no means. But, I would ask the neighbors across the street what they used to control weeds, and what fertilizer they used since they look good from what I can see. Good luck.

Can you please post a closeup of the trouble area, as well as a closeup(3 inches away) of a healthy area so we can determine what type of grass you have?

The tree appears to be higher than the lawn. Could it possibly be due to water runoff? Just a thought.

It's likely to be fescue and/or rye grass. Both of those grow in clumps. If they thin out then you'll see thinning (space between the remaining clumps). Thinning is caused by kids or pets playing on it, disease, and/or insects. You fix that by either of two ways. One popular thing to do is to seed in some Kentucky bluegrass. KBG does not grow in clumps. It spreads to fill in thin areas. The other alternative is to overseed the thin areas every FALL (not spring or summer).

Now is the time to spot spray the dandelions and other broadleaf weeds. Use a product like Weed b Gon or Weed b Gon Chickweed, Clover, and Oxalis Killer. That will leave you with grass and grassy weeds (like crabgrass and some others). Then take good care of that until fall when you can reseed the thin or weedy areas with either fescue, rye, or KBG.

Yes tilling is a lot of work. Next time NEVER rototill in preparation for new grass. You might already hate yourself for tilling. Why? Because the soil is not firm enough and is settling unevenly. Your lawn will become bumpier and bumper for the next 3 years as the soil settles and firms up. Besides that you did all this work in the spring. Spring seeding is a problem because the new roots are not strong enough for the summer heat. If your summers are cool you might get away with it. The other issue in the spring is that is the time crabgrass seed is germinating. It is very easy to end up with 100% crabgrass by July. Don't kick yourself for this. Just take care of whatever you get and fix it in the fall. Summer weeds die in the fall anyway.

You should not be watering every week.

Watering: Deep and infrequent is the mantra for watering. This is for all turf grass all over the place. Deep means 1 inch all at one time. Put some cat food or tuna cans around the yard, and time how long it takes your sprinkler(s) to fill all the cans. Memorize that time. That will be the time you water from now on. My hose, sprinkler and water pressure takes 8 full hours to fill the cans. Your time will likely be less. I like gentle watering. As for watering frequency, that depends on the daytime air temperature. With temps in the 90s, deep water once per week. With temps in the 80s, deep water once every 2 weeks. With temps in the 70s, deep water once every 3 weeks. With temps below 70, deep water once a month. Note that you have to keep up with quickly changing temps in the spring and fall. This deep and infrequent schedule works in Phoenix and in Vermont, so it should work for you. The reason for deep and infrequent is to grow deeper, more drought resistant roots and to allow the soil to dry completely at the surface for several days before watering again. If it rains, reset your calendar to account for the rainfall.

You can put down the first fertilizer of the year on Memorial Day.

Thank you all so much for the advice-- I clearly still have a lot to learn, but you've all been so helpful in getting me started in the right direction!