In a small saucepan over medium heat, combine the blueberries, 2 tablespoons. of the sweetener, and water. Cook, stirring occasionally, until the blueberries have softened and released their juices, about 5-7 minutes (if using frozen blueberries add extra minute or two). Allow the mixture to cool slightly, then puree it using a blender or food processor until smooth. Set aside to cool completely. In a separate bowl, mix the Greek yogurt, the remaining 1 tablespoon of sweetener, honey (or alternative sweetener), and vanilla extract until well combined.
To assemble the popsicles, spoon a layer of the yogurt mixture into the bottom of each popsicle mold. Add a layer of the blueberry puree on top, then continue to alternate between the yogurt and blueberry layers until the molds are filled. Use a skewer or the handle of a spoon to gently swirl the layers together for a marbled effect.
Insert popsicle sticks into the molds, then freeze for at least 4 hours, or until the popsicles are firm.
To release the popsicles from the molds, run warm water over the outside of the molds for a few seconds, then gently pull the popsicles out.