Recent advances in artificial intelligence (AI) have shown promising results in various image-based systems, improving accuracy and throughput, while reducing latency. All these factors are crucial in healthcare and have generated increased interest in this technology. However, there are also multiple challenges integrating AI in existing systems, such as poor explainability, data imbalance and bias. These challenges affect the reliability of the neural networks used in AI applications. The limitations may significantly affect the quality and cost of medical care by introducing false positive diagnosis. The false positives subsequently lead to increased stress in patients and necessitate additional testing and procedures. Lack of rich data representing all socio-economic groups can also undermine reliable decisions for underrepresented groups. Although various studies discussed techniques that may help with bias mitigation, to the best of our knowledge, no practical experiments have been conducted so far that compare different reweighting approaches using convolutional neural networks (CNN). This work focuses on in-depth explanatory analysis of chest X-ray datasets to understand and quantify the problem of class imbalance and bias. After that, various topologies of binary classifications are compared, followed by practical applications of loss reweighting techniques and comparison of their influence of privileged, underprivileged, and overall population. Experiments proved that high classification accuracy can be achieved using an efficient model topology suitable for embedded devices, making it possible to run locally without the need for cloud processing. Preliminary results showed that performance of the model for the underprivileged class can be improved by 15% if proper weighting factors are obtained and applied during the training procedure.