Saute beets in margarine in Dutch oven 3 to 4 minutes. Add stock cabbage, carrots, garlic, bay leaf, sugar, and vinegar. Heat to boiling. Reduce heat and simmer, covered, until vegetables are tender, 20 to 30 minutes.
Cook sausage links in lightly greased skillet over medium heat until browned on all sides, about 5 minutes. Cut links into 1-inch pieces and stir into soup; cook 5 minutes. Season to taste with salt and pepper, sprinkle each bowl of soup with dill weed.