Answer: If you read the labels carefully, you will find you will not be able to use a "weed and feed" type of product or spread a weed killer product for several months after planting the new grass. You could spot treat some of the weeds with an herbicide containing glyphosate. Read and follow the label directions. Be careful using it as it will kill grass as well as weeds.
You may find that correct mowing helps the existing grass to fill in. Mow at three inches. Mow often enough that you never remove more than one third the grass height at a time. This may mean mowing more than once a week in the spring.
Correct fertilizing can also enhance the grass growth. Run some basic tests to check the fertility and also check the soil pH to see if you need to lime. Then add fertilizer and lime as indicated by the test results. (Correcting the pH allows the grass to use the fertilizer better.)
Surprisingly, late summer is the best time to do extensive lawn work. If by then the lawn is not looking better after a season of good care, then you could consider doing some additional work on it.
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