Chickweed is a winter annual and will die in summer.

Any herbicides you apply now will kill the new grass that was just seeded.

Your biggest problem is your watering schedule. Think about it for a second. When you seed a new lawn, what are you supposed to do? - Water, water, water. That is how you get seeds to germinate. You are doing that on a slightly smaller scale, but weed seeds typically germinate easier than grass seed. The result is basically the same - lots seeds germinating!

As a long term weed control plan, you should have a basic plan that includes:

1) Doing seeding in fall - most weeds germinate in the spring.
2) Getting as much healthy grass growing as possible before winter so that you aren't disturbing the soil in spring.
3) Watering deeply but infrequently. Ideally, that means 1" of water put down all at once. If the soil is really sandy, you might need to make that 1/2" twice a week.
4) Mowing the grass high - 3"+.

Thanks for the reply Bill. I don't think the new grass is even germinating since they applied pre-emergent a few weeks prior to the seeding. I wish they hadn't done it. Since writing this I turned off the watering, it has been cool here anyway.

So I guess I shouldn't spray the weeds now? I am just so afraid of them taking over the grass I do have, it was not easy to get to this point. FYI this is the mouse eared variety, not sure if that matters.

If they applied a preemergent,then the new grass isn't going to germinate. Go ahead and treat the weeds now if you want. A simple weed-b-gon spray will work just fine. chickweed is very shallow rooted, so you could also just spend a couple hours pulling it up.

Most of the common preemergents work for months, so you are out of luck seeding this year.

Fortunately for you, bluegrass spreads. If you have "some" mixed in with the weeds, it will fill in as the year goes on as long as you care for it properly. After summer passes, you can spot seed any thin areas.

If you are trying to limit the use of chemicals, I suggest the "On the way in" method of weeding. As soon as you get home from work, go out and pull 25 weeds. It will only take 5 minutes but over a season, that adds up to 2,000 weeds.

LOL..I weed on the way in..on the way out..and randomly in between! For every 25 weeds I pulls it seem 50 pop up in their place.

I guess I will spray now. Should I try spreading a layer of peat moss over the grass to amend the soil? in fall apply a pre-emergent to hopefully stop next springs round from popping up?

If you are going to spread of layer of anything to help the soil, go with compost instead of peatmoss.

Seeding and preemergents don't mix. If you seed in the fall, then you don't use a preemergent.