Traditional software fairness research typically emphasizes ethical and social imperatives, neglecting that fairness fundamentally represents a core software quality issue arising directly from performance disparities across sensitive user groups. Recognizing fairness explicitly as a software quality dimension yields practical benefits beyond ethical considerations, notably improved predictive performance for unprivileged groups, enhanced out-of-distribution generalization, and increased geographic transferability in real-world deployments. Nevertheless, existing bias mitigation methods face a critical dilemma: while pre-processing methods offer broad applicability across model types, they generally fall short in effectiveness compared to post-processing techniques. To overcome this challenge, we propose Correlation Tuning (CoT), a novel pre-processing approach designed to mitigate bias by adjusting data correlations. Specifically, CoT introduces the Phi-coefficient, an intuitive correlation measure, to systematically quantify correlation between sensitive attributes and labels, and employs multi-objective optimization to address the proxy biases. Extensive evaluations demonstrate that CoT increases the true positive rate of unprivileged groups by an average of 17.5% and reduces three key bias metrics, including statistical parity difference (SPD), average odds difference (AOD), and equal opportunity difference (EOD), by more than 50% on average. CoT outperforms state-of-the-art methods by three and ten percentage points in single attribute and multiple attributes scenarios, respectively. We will publicly release our experimental results and source code to facilitate future research.