Hydrophilic and hydrophobic weak polybasic brushes immersed in aqueous solutions of mixed salt counterions are considered using a mean-field numerical self-consistent field approach. On top of the solvent quality of the polymer, the counterion-solvent interactions are accounted for by implementing Flory-Huggins interaction parameters. We show that ion specificity within the brush can bring about large changes in conformation. It is found that the collapse transition of hydrophobic, weak polyelectrolyte brushes features an intermediate two-phase state wherein a subset of chains are collapsed in a dense layer at the substrate, while the remainder of chains are well-solvated and strongly stretched away from the it. Besides pH and ionic strength, solvent quality of counterions and the composition of ions in the solvent are important control parameters for the behavior of polyelectrolyte brushes. Increasingly hydrophobic counterions penetrate deeper within the brush and stabilize the collapsed region, while hydrophilic counterions do the opposite.