Combine water and 1/2 cup sugar in a microwave-safe glass measuring cup. Microwave at HIGH 2 1/2 minutes, stirring to dissolve sugar; cool.
Combine syrup, tequila, Grand Marnier, fresh lime juice, and blackberries in a blender; process until smooth.
Strain mixture through a cheesecloth-lined sieve over a pitcher; discard solids.
Combine 1 1/2 tablespoons granulated sugar and kosher salt in a dish. Cut lime into wedges; rub rims of 4 glasses with lime wedge. Dip rims of glasses in salt/sugar mixture. Serve margaritas over ice. Garnish with fresh blackberries and lime wedges.