Important applications of advancements in machine learning, are in the area of healthcare, more so for neurological disorder detection. A crucial step towards understanding the neurological status, is to estimate the brain age using structural MRI volumes, in order to measure its deviation from chronological age. Factors that contribute to brain age are best captured using a data-driven approach, such as deep learning. However, it places a huge demand on the availability of diverse datasets. In this work, we propose a robust brain age estimation paradigm that utilizes a 3D CNN model, by-passing the need for model-retraining across datasets. The proposed model consists of seven 3D CNN layers, with a shared spatial attention layer incorporated at each CNN layer followed by five dense layers. The novelty of the proposed method lies in the idea of spatial attention module, with shared weights across the CNN layers. This weight sharing ensures directed attention to specific brain regions, for localizing age-related features within the data, lending robustness. The proposed model, trained on ADNI dataset comprising 516 T1 weighted MRI volumes of healthy subjects, resulted in Mean Absolute Error (MAE) of 1.662 years, which is an improvement of 1.688 years over the state-of-the-art (SOTA) model, based on disjoint test samples from the same repository. To illustrate generalizability, the same pipeline was utilized on volumes from a publicly available source called OASIS3. From OASIS3, MRI volumes 890 healthy subjects were utilized resulting in MAE of 2.265 years. Due to diversity in acquisitions across multiple sites, races and genetic factors, traditional CNN models are not guaranteed to prioritize brain regions crucial for age estimation. In contrast, the proposed weight-shared spatial attention module, directs attention on specific regions, required for the estimation.