Make several shallow slashes in skinless side of salmon. Place filets skin-side down in a glass baking dish.
Whisk together brown sugar, garlic, olive oil, onion, pepper, rice vinegar, sesame oil, and soy sauce. Pour over salmon, cover and refrigerate 2 hours. 1 hour is enough. 2 is better.
Preheat the oven to 350 degrees F (175 degrees C).
In medium saucepan combine the dill weed, rice, and water. Bring to a boil, then cook over medium low heat about 20 minutes. Rice should be tender. Water should be absorbed.
Remove cover from salmon, and bake for about 30 minutes. Salmon is done when it can be flaked with fork.
To serve, place salmon on a bed of rice and drizzle sauce over it.