Cut salmon in half crosswise. Stir together salt, sugar, lemon zest, and pepper in a small bowl. Sprinkle salmon halves on all sides with salt mixture. Place 1 piece of salmon, skin side down, on a large piece of plastic wrap. Top with dill sprigs; place remaining piece of salmon directly on top, skin side up. Wrap salmon tightly with plastic wrap, and place in a large baking dish. Place a cast-iron skillet directly on top of salmon. (Or use a large plate weighted with cans.)
Chill 24 hours. Turn salmon over; replace weights, and chill 24 hours.
Remove weights and plastic wrap, discarding wrap. Drain and discard any liquid, and discard dill sprigs. Thinly slice salmon; serve with toasted pumpernickel triangles, Citrus Crème Fraîche, and caviar; garnish with dill.