Add the blackberries and water to a medium saucepan. Cook over medium heat, stirring periodically, for about 10 - 15 minutes, or until they are easily broken with a wooden spoon. Taste and add sugar to sweeten if needed. Stir sugar in and cook until dissolved.
Pour the berry mixture into a powerful blender, such as a Blendtec, and puree until very smooth. I ran the "whole juice" pre-programmed functioin on my blender. After blended, cover and refrigerate the blackberry puree until cool, at least 30 minutes.
While the blackberry mixture refrigerates, beat the cream cheese, milk, lime juice, zest (if using), vanilla, and sugar using a hand mixer or puree with a small food chopper until smooth. Set aside in the refrigerator until blackberry mixture has cooled.
To assemble popsicles, layer the blackberry puree and cream cheese mixture in popsicle molds. Place popsicle sticks in the center and freeze until solid.
If necessary, run hot water over the outside of the molds to assist in removing the pops before serving.
A high powered blender will crush the seeds, but if you prefer a completely smooth fruit layer with no bits of seeds then strain the blackberry puree through a fine mesh strainer. Layering Options:
We experimented with a couple layering techniques. I preferred #1 with smaller amounts of each layered more frequently, while Eric preferred #3.
1. Cream Cheese, Blackberry, Cream Cheese, Blackberry
2. Blackberry, Cream Cheese, Blackberry
3. Combine the two mixtures and swirl together.