Monte Carlo simulation has been used to study titration and configurational properties of an isolated hydrophobic polymer containing weakly-ionizable groups. Using a cubic lattice, simulations were performed in the grand canonical ensemble to include the effect of the local charge environment on the ionization of weak electrolyte segments. Properties were studied as a function of polymer hydrophobicity, fraction of ionizable segments, solution ionic strength, and pH. The polymer segments experienced three types of competing interaction: excluded volume, attractive nearest-neighbor forces which account for the net balance of segment-segment, segment-solvent, and solvent-solvent interactions, and long-range electrostatic forces between ionized segments, calculated with a screened Debye-Hückel potential. Simulations show that the model chain expands with chain ionization, which depends on solution pH. As the chain becomes increasingly charged, the ionization process becomes more difficult because of rising local charge density around the ionizable segments. The effect of rising local charge density increases for larger fractions of ionizable groups, with increased hydrophobicity and with low ionic strength.