In a food processor or blender, puree 4 oz of the blackberries until smooth.
Strain the blackberries through a fine mesh strainer and set aside.
Preheat oven to 350 F. Line 8x8 pan with parchment paper, making sure that the sides extend over the pan.
In a medium bowl combine crushed graham crackers, sugar, and melted butter.
Press into pan and set aside.
Beat cream cheese and sugar until fluffy.
Add the eggs, vanilla extract and sour cream. Beat just until smooth.
Pour cheesecake evenly into prepared crust.
Press halved blackberries into cheesecake batter, making sure that the blackberries are all the way down and are covered by the cheesecake batter.
Place dollops of blackberry puree all over the cheesecake batter and swirl with a butter knife.
Bake cheesecake for 35-45 minutes or until edges are set, but the center is still a little bit jiggly.
Let the cheesecake cool before removing from pan. Chill the cheesecake in the refrigerator at least 4 hours before serving.
