Combine bacon fat, lemon juice, garlic, salt, pepper, brown sugar, and thyme together in a bowl. Spread a small amount of the bacon fat mixture in bottom of baking dish. Lay snapper fillets into baking dish; cover with remaining bacon fat mixture. Cover baking dish with plastic wrap and marinate in the refrigerator, about 1 hour.
Preheat oven to 350 degrees F (175 degrees C). Spray a baking dish with cooking spray.
Remove plastic wrap from baking dish; add tomatoes, onions, and Worcestershire sauce.
Bake in preheated oven until fish flakes easily with a fork, 40 to 60 minutes. Garnish with parsley.