The best natural weed killer is to pull the weeds by hand.

Vinegar can be sprayed and will kill any grass or weed that cannot handle acid.
Baking soda can be sprayed and will kill any grass or weed that cannot handle alkaline.
These two methods work very poorly. I have tried both, the weeds and grass turns black, the leafs die but does not kill the roots, so the weeds grow right back.

Weed or till frequently.

Consider feeding organically (I do). Unlike synthetics, the nitrogen isn't water soluble and doesn't easily wash down into the water table and then into your drinking water.

For weeds, a well-fed, high-mowed lawn is less likely to allow weed growth. You can pull the few you do get by hand.

It would be helpful to have some more information. You're assuming you have to have weeds and use weed killers. You don't have to have weeds, so if you could answer some questions we could figure out why have have weeds to begin with.

Where do you live?
What kind of grass do you have?
What weeds do you have (grassy or broadleaf)?
How are you watering (how often and for how long)?
How high/low are you mowing?
When were the last 2 times you fertilized and what did you use?

I absolutely agree with organics. If you're concerned about the water then you might be concerned about using Milorganite. Milorganite is semi-processed sewage from Milwaukee. I use alfalfa pellets (rabbit chow) because it is rather inexpensive for me. You might use soybean meal if that is less expensive. The application rate is 20 pounds per 1,000 square feet. You can use it as often as you want.