Roast the beets, peel, and cut in wedges or slice into half-moons.
Stir together the vinegar, sugar, olive oil, and salt and pepper to taste. Toss with the warm beets and allow to marinate for 2 to 3 hours at room temperature or in the refrigerator.
Place the garlic in a mortar and pestle, add ⅛ teaspoon salt, and mash to a paste. Stir into the yogurt in a small bowl. (OR grate the garlic on a fine microplane style grater and add with the salt to yogurt). Stir in half the dill. Add salt and pepper to taste.
Drain the beets and stir some of the marinade into the yogurt (to taste).
Toss yogurt with the beets, or arrange the beets on a platter and drizzle the yogurt over the top. Sprinkle on the remaining dill, and serve.