Convolutional neural networks (CNNs) have succeeded remarkably to attain improved performances compared to conventional feature descriptors for histopathology image classification. Several previous works used pre-trained backbone CNNs and applied ensemble techniques which increased computational complexity. To address this issue, we propose a new CNN incorporating a weighted attention module to boost feature representation power. The proposed CNN is developed with separable convolutional blocks with a reduced computational complexity for surpassing cancer multi-classification performance. An attention-based feature weighting scheme is included for refining the effectiveness of high-level feature representation. Also, a squeeze and excitation module is injected for channel-wise feature calibration. The proposed method is evaluated on publicly available BreakHis histopathology dataset with 40 \(\times \) and 100 \(\times \) magnifications implying breast cancer, and LC25000 dataset for lung-colon cancer. The average test accuracy of five-fold cross validation using proposed CNN on the BreakHis 40 \(\times \) is 93.50%, 88.14% on the BreakHis 100 \(\times \) , and 99.26% on the LC25000 dataset. The proposed CNN is built with only 11.34 millions model parameters implying its computational benefits. Overall, the proposed CNN enhances feature computation abilities for improving the classification performances of cancer subtypes.