Preheat oven to 275°.
Place parchment paper over 2 baking sheets. Draw 3 (8-inch) circles on paper. Turn paper over; secure with masking tape.
Beat egg whites, cream of tartar, salt, and vinegar with a mixer at high speed until foamy; add vanilla. Slowly add sugar, 1 tablespoon at a time, beating until stiff peaks form and sugar dissolves (about 2 to 4 minutes).
Divide meringue evenly among 3 drawn circles. Spread evenly into circles using the back of a spoon. Bake at 275° for 1 hour or until dry. Turn oven off; cool in oven at least 4 hours. Carefully remove from paper.
Combine chocolate chips and water in a small microwave-safe bowl. Microwave at HIGH 35 seconds; stir until smooth. Set aside (do not allow to cool).
Place 1 meringue layer on a serving plate. Carefully spread 1/2 of melted chocolate onto meringue. Spread 1/3 of whipped topping over chocolate; top with 1/2 cup strawberries and 1/2 cup blackberries. Repeat layers once. Top with the third meringue, and spread with remaining whipped topping. Cover and chill at least 3 hours before serving. Garnish with additional strawberries and blackberries before serving, if desired.