If your lawn is healthy and happy it will not have a weed problem. Getting your lawn healthy and happy starts with the renovation that we just went through. Keeping it that way should start with a regular application of organic fertilizer. Organic fertilizers are not a flash in the pan treatment. They help to rebuild the soil by reactivating the micro-organisms in the soil.
Chemicals do just the opposite.
When you water your lawn, water deeply. Apply at least one inch of water to each area before moving the sprinkler. Place a coffee can in the path of the sprinkler to measure the water. Shallow watering is not good. It promotes shallow roots, which makes for a lawn that is vulnerable to all kinds of problems, especially drought.