Wash rice thoroughly and combine 2 cups rice with 4 cups water in a medium saucepan; bring to a boil.
Reduce heat, cover, and simmer until water is absorbed, about 20 minutes.
Remove cores from both cabbage heads using a thin, long knife.
Place one cabbage in a microwave-proof container with the cored part down; add ½ cup water, cover, and microwave on high for 10 minutes.
Turn cabbage over, cook covered for another 10 minutes, then let cool and carefully separate leaves, removing tough ribs.
Repeat the steaming process with the second cabbage.
Sauté half of the chopped onions in 3 tablespoons butter until translucent; do not brown.
In a large bowl, combine the cooked rice, uncooked ¾ cup rice, sautéed onions, remaining raw onions, ground beef, pork sausage, garlic, dill weed, salt, black pepper, and sugar; mix well.
Spoon about 2 tablespoons of the filling onto each cabbage leaf, then roll and tuck in the ends to secure.
Preheat the oven to 350°F (175°C).
Line the bottoms of two 9x13-inch casserole dishes with leftover cabbage leaves, then arrange the cabbage rolls tightly in a single layer.
Purée the canned tomatoes and condensed tomato soup together until smooth.
Pour the tomato mixture over the cabbage rolls until just covered.
Place 4 bay leaves on top of the sauce in each dish and cover dishes tightly with foil.
Bake for 2 hours, then remove from oven and let cool for 15 minutes before removing foil.
Serve the cabbage rolls hot.