Combine 1 1/2 tablespoons of sugar and kosher salt on a small plate. Rub a wedge of lime around the rim of each glass and dip in the sugar/salt mixture.
Combine water and 1/4 cup sugar in a glass bowl and microwave for 30 seconds to 1 minute. Stir to dissolve sugar. Let cool.
In a blender, combine syrup, lime juice, tequila, Grand Marnier, and blackberries. Process until smooth.
Strain mixture through a fine-mesh sieve into a small pitcher.