Most weeds are opportunists. If your grass is not doing well, weeds will proliferate. Aerate your lawn by pulling plugs of soil out of your lawn. Go over it as many times as you can. Allow the plugs to disintegrate on top of your...lawn. Get a soil test done. Find out what nutrients are low, high, acceptable and what the pH of your soil is...do you have 1" of thatch or more? If so you might need to power rake up the thatch and remove it.
After the four weeks are up and you've gotten your tests back you will have the information you need to regrow your lawn. The pH should be 6.5-7.0. If not, apply lime. Use half the amount recommended. You want to raise the pH slowly in stages if possible. Buy the best lawn seed available. On the label you should see 'weed seed = zero'...make sure this seed is for your area.
Before spreading seed, I'd put fertilizer down. The absolute best stuff I have used is by Dr. Earth...lawn fertilizer. I am sure there are other products similar by now but they should be organic, extended release, have the proper amounts of NPK for your lawn soil (according to your soil tests), micronutrients and bacteria (one of these bacteria will help decompose thatch) to innoculate your soil with beneficial life.
Use a spreader for the fertilizer and apply the correct amount. It will be more than you are used to if you've been using inorganic fast release fertilizers. I think it is 9# per 1000 versus 5# per 1000 sq.ft.
If you've thatched and/or aerated, there should be enough soil to seed. You don't want too much soil or mulch dumped on top of your seed or it won't germinate. You want your seed in contact with soil, not mulch. Your soil could probably use the organic matter but you can do that later when your lawn is more mature. Also, test your soil again for pH. If it is below 6.5, add more lime. Never apply lime without testing first.
Apply the seed with your spreader, in the amount suggested on the package. Don't throw it on by hand and don't over-apply, either. Rake lightly with a leaf rake and then roll.
Keep the top continually moist. It might mean you water 2 or 3 times a day. Do not saturate. This takes almost 2 weeks. Allow the soil to dry a bit before your first mowing. Gradually allow the soil to dry out between waterings to train your lawn to have deep roots and becomes drought tolerant. Aim for once per week watering. When you water make sure the amount is enough to wet the soil 4-6" deep. Don't water again until your footprints in the grass are clear and the blades stay down. Then water deeply. And water during the day so that your grass isn't wet at night. This will prevent disease.
Mowing. Not sure where you live but if your grass is like ours in the Pacific Northwest, never mow below 3". These grasses have large root systems, genetically. If there isn't enough top growth to feed these roots, your grass will not thrive and the weeds will be back. Always make sure your blades are sharp. If you miss a week of mowing and the grass has gotten long, take it down in stages. Don't cut more than 1/3 of the height in one cutting. And remove the clippings. I haven't got much trust in mulching mowers. If this were a huge pasture I wouldn't remove clippings, but if you've invested all this effort, I'd use the clippings in my compost, to be used after decomposed.s
Your lawn should look lush and dark green. The 3" height will shade out weed seeds and help to preserve moisture.
Fertilize at least twice a year. The percentages of the nutrients are different from spring to summer and fall. Aerate once per year. Add a thin layer of compost after aeration. Water deeply and allow to dry out before watering again.
You shouldn't have to ever use an herbicide again.