For the berry "jam': Put the berries in a small heavy saucepan. Sprinkle the sugar over them and mash together with a fork until the berries are coarsely mashed and juicy. Heat the berry-sugar mixture over medium-low heat, stirring frequently, until thickened, about 15 minutes.
To make the popsicles: Stir the yogurt, milk and honey together until blended. Spoon enough of the yogurt into the molds to fill about one-fifth. Add a layer of berries, then yogurt, then berries, then yogurt up to the fill line. Use a butter knife to swirl the yogurt and berries together but don’t over-swirl. Put the popsicle handles into the mold and freeze until solid. This can take from 4 to 6 hours, depending the type of mold you use.
Remove and enjoy.
Notes
Feel free to use anything you have instead of a proper mold. Paper cups, silicone muffin tins. As long as you have sticks you are good togo!