Combine the granulated sugar and 1 cup water in a saucepan and bring to a boil. Cook until the sugar is dissolved. Add the cranberries and weight with a plate to submerge. Cover the pot and refrigerate for at least 8 hours and up to 48 hours. Strain the cranberries, reserving the syrup. (Refrigerate leftover syrup in an airtight container for up to 1 month.)
Spread the superfine sugar on a baking sheet; toss the cranberries in the sugar. Refrigerate on the baking sheet, uncovered, for 1 hour. Toss again in the sugar before transferring to an airtight container. Refrigerate until ready to serve.