The flavor of the fruit is most often related to the variety of plant you have. Some types of blackberry plant naturally produce more tart fruit. You can improve the quality of the fruit by using organic mulch around the plants. The mulch keeps in moisture and feeds the soil and will ultimately improve the quality of the fruit. The more tart berries are good for jams and pies as sugar can be added to counteract the tart flavor of the berries. If you want sweeter berries you may have to try a different variety.