Frequent watering is exactly what weed seeds need to sprout. When you allow the soil to dry out at the surface, many weeds will never germinate.

First measure how much water your grass is getting. Put out a tuna or cat food can and collect the water for the time you are watering. Eventually you will be applying on the order of an inch per week in the summer and an inch per month in the cooler seasons. My sprinkler, hose, water pressure combination applies 1/8 inch per hour over 900 square feet. That's not much. I have to water for 4 hours to get 1/2 inch.

I would wean it off the daily watering. Since you are only wetting the surface, the roots will only be at the surface. You need to encourage them to dig a little deeper every time you water. Start by watering twice as long and skipping a day. Do that for a week watching it for signs that it is wilty. Don't let it wilt. Then try every third day and water a little longer. Remember you are toward once per week and only enough water so that the turf will survive for the next week. How much you water and how often is determined by your soil, shade, clouds, humidity, rainfall, grass type, mowing height (short grass needs more water), and wind.

When you are increasing the amount of water you apply, don't let the water runoff. If you see runoff, stop watering and let it soak in for 30 minutes, then resume watering. If it never seems to want to soak in, then before you water the next time, spray your lawn with baby shampoo. I use a hose end sprayer and adjust it so you just see foam coming out. Spray it evenly and then irrigate. You are not trying to irrigate with the baby shampoo, just get it out there. Baby shampoo is a good way to open up the soil and allow it to absorb moisture better. You might have to repeat every other week for a few months. Or not. For me one app is enough to last months.

Thank you for the feedback. I'm looking forward to trying this and getting my grass's root system to root better and make the most out of the watering.