1. Place a rack in center of oven and another 2 rungs below; preheat to 325°F. Fill a 9-by-13-inch baking pan with 1 inch water. Line a 12-cup muffin tin with cupcake liners and mist with cooking spray.
2. Mix graham cracker crumbs, 2 Tbsp. sugar and 1 egg white in a bowl until evenly moistened. Spoon 2 rounded teaspoonfuls into each muffin cup. Press evenly to form a firm crust. Bake until golden and slightly puffed, 5 to 8 minutes. Let cool on a wire rack.
3. Using an electric mixer on low speed, beat cream cheese in a bowl until smooth. In a separate bowl, mix remaining 6 Tbsp. sugar, flour and lemon zest; add to cream cheese. Mix on low speed until just combined. Scrape down sides of bowl. On medium speed, mix in yogurt, vanilla, whole egg and remaining 2 egg whites, one at a time, until smooth. Divide cream cheese mixture among muffin cups (about 1/4 cup for each). Place pan on middle oven rack. Place baking pan filled with water on rack below. Bake until cheesecakes are slightly puffed, 25 to 30 minutes. Let cool to room temperature in pan on a wire rack, then refrigerate for at least 1 hour.
4. Before serving, top each cheesecake with 2 to 4 blackberries. Mix remaining berries, preserves and 2 Tbsp. water in a small pan; bring to a boil over medium heat. Cook, stirring occasionally, until berries are soft and sauce has thickened, 3 to 4 minutes. Cool slightly. Spoon 1 Tbsp. glaze over berries.