Place fruit and cinnamon stick in a sterilized pint jar. Bring vinegar just to a boil; pour over fruit, leaving 1/4-in. headspace. Center lid on jar; screw on band until fingertip tight. Refrigerate for 1 week., Strain vinegar mixture through a fine-mesh strainer into another sterilized pint jar. Press solids to extract juice; discard remaining fruit., Bring sugar and water to a boil. Reduce heat; simmer until sugar is dissolved. Cool slightly. Stir into vinegar mixture; shake well. Store in the refrigerator up to 2 weeks. , To serve, drink 1-2 tablespoons or add to a glass of ice, top with sparkling water and garnish with fresh blackberries.