Domesticated blackberries have been bred to produce large fruits. Ensure that your blackberries have sufficient water so the soil is moist (not soggy) when they are producing berries.
Also, you can fertilize them to keep them at their peak.
Pruning is important so that the plants put their energies into fruit and not just foliage. Here is Cornell's fruit growing guide. http://www.gardening.cornell.edu/fruit/homefruit/homefruit.pdf
Read over the info under Brambles. Especially look at p. 73 for pruning information. Your wild blackberries are thorny and should be pruned as for "thorny blackberries."