Absolutely post a picture. Take pix on cloudy days if you can to reduce the contrast from the sunlight. Also take one looking across the yard and one from about 3 inches above the grass. 3 INCHES, not 30 inches.

Mowing low might have been perfect for your grass. Or it might have been holding it back. From what you've described, I'm not sure what you have that would be weed free with that kind of care.

Are you interested in an organic approach? The way I do it the cost is about the same as chemicals, but you don't have to hassle with what fertilizer to use when and what ratios and do I have to water it in and can I apply in the summer and several other issues that don't come to mind off hand.

General lawn care goes like this:

Watering
Deep and infrequent. Deep means 1 full inch all at one time. measure how long it takes to apply an inch by setting cat food or tuna cans out in the yard and turning on the sprinklers. Infrequent means once every 3 weeks with temps in the 70s. Once every 2 weeks with temps in the 80s. And once every week with temps in the 90s. Watering like this will give you a strong root system that resists drought. It also helps fight off weeds by not keeping the soil surface moist all the time.

Mowing
Generally mow high except for bermuda, centipede, and creeping bentgrass. Those should be mowed at the lowest setting. Post a pic of your grass and we can help to identify it.

Fertilizer
Unless you have bermuda, then you can fertilize once in late May (Memorial Day is good), once in early September (Labor Day), and once in late fall (Thanksgiving is usually good).

If you have broadleaf weeds, spot spray with Weed-B-Gone...unless you have St Augustine (commonly called carpet grass). If you have St Aug, the WBG will kill the St Aug. You have to use something else for that. Send a pic. If you have grassy weeds, either pull those or you could spot spray with RoundUp. That is a tough love approach because the RoundUp is guaranteed to kill the surrounding grass. The benefit is the weed is gone and the surrounding grass should refill the dead spot.

Plugging will probably work and this is a good time. How big would the plugs be? I'm thinking 10x10 inches would be minimum for St Augustine patches. St Aug should spread fast if you give it the right care. I've had excellent success with it covering several thousand square feet in two seasons.