Be especially careful to keep newly planted stock well watered. Keep after the sprouts by either cutting them off as they appear or by painting them with a brush killer. Be careful if you use a herbicide, because many can damage other broadleafed plants or your grass. Be persistent and sooner or later the roots will die. It looks like blight.
Blight usually means a fungus disease.
Your tomatoes have blossom end rot, which is caused by a lack of calcium in the developing fruit. In very hot, windy weather tomato plants have trouble supplying enough calcium. No spray will help. Keep the ground evenly moist to minimize the condition. It is worse on staked tomatoes and on some varieties.