I'm with you on the weed control, and for nutrients this technique will help you too, though long term- meaning next season.
After we put in our plants, lay down about 3 or 4 layers of newspaper sheets, opened up, around them. Our local paper is printed in soy ink, so no worries on chemicals. Just make sure you do not use the "slick" or advertisement sections...different paper and chemicals. Then we cover with 4 to 6 inches of straw and make sure it's wet down well so the newsprint conforms to the ground beneath it and stays moist. It will block all sun to the weeds and prevent any germination while working with the straw to keep the ground damp all summer long, even in august. If you plant seeds (like in our cucumber rows in pic below) just leave the area clear. The plants will soon enough take over and block out weeds. In this pic, cucumber seedlings to the left, tomatoes to the right-
This method has worked well for us and makes the garden look nice all summer long. The best part about it is that by late fall, the newsprint has disintegrated into the soil, the lower portion of the straw has too, and you can just till up everything in the early spring to replenish the garden. Looks well tended, and not a bit of weeding all season.