Place the blackberries and sugar in the blender. Blend on high speed until smooth.
Place a fine mesh strainer over a bowl and pour the blackberry puree in and press it through with a spoon, leaving the seeds behind.
Spoon the blackberry puree and the yogurt in the popsicle molds, making layers as you go.
Insert the sticks and freeze for at least 4 hours until firm.
Notes
This recipe is easy to double or even triple to accommodate the size and shape of your popsicle mold.Store popsicles in the freezer for up to 2 months.