Properly stored blackberries will keep in the refrigerator for up to 3 days.
After 3 days in the refrigerator the blackberries will likely start growing mold and should be thrown out.
If you want to extend the shelf life of your blackberries don't wash the blackberries until you're ready to eat them.
If you notice any blackberries that are bruised remove them from other other blackberries before refrigerating them.