Combine first 3 ingredients in a shallow dish, stirring until sea salt and sugar dissolve; add fish. Let stand 20 minutes. Drain; pat dry.
Prepare charcoal fire in a chimney starter; let coals burn for 15 to 20 minutes or until flames die down. Carefully pour hot coals out of starter; pile on one side of grill. Alternately, preheat a gas grill, turning one side to high heat and the other side to medium heat. Coat grill grate with cooking spray; put grate in place.
Sprinkle 1⁄4 teaspoon salt and pepper over fish flesh. Divide dill and lime slices evenly among fish cavities.
Coat outside of fish with cooking spray. Place fish over direct heat (the hot zone); grill 4 minutes.
Turn fish over and move to indirect heat (the cool zone). Grill 12 minutes or until done.
Recipe Notes
Easy does it when turning fish on the grill. To avoid tearing the skin, gently roll the fish over with a spatula instead of turning it with tongs.