Objective: Clinical radiography needs automated X ray disease classification, especially in resource on strained settings. The primary aim is to improve diagnosis accuracy and reduce the manual burden on medical professionals. Existing methods have trouble combining information from different scales of features while simultaneously lowering the computational complexity. This makes it difficult to capture complex spatial and channel-wise correlations. Method: A novel and extremely lightweight HACNet model with just a million parameters has been proposed to overcome these limitations. It contains a novel Hierarchical Attention-Compression Module (HACM) to boost feature representational capacity. A Feature Aggregation Unit (FAU)combines different feature maps using close connections and a Triplet Attention layer, while the Attentional Compression Unit (ACU) simplifies the data by using stride convolution along with channel and spatial attention methods. Results: Results of experiments concerning the Covid-19 radiography dataset and the ChestX ray8dataset demonstrate strong classification capabilities of the suggested model in identifying diseases from x-ray images. The suggested model is more computationally efficient than popular computer vision models and demonstrates excellent qualitative capabilities, as demonstrated by t-SNE plots.