Prompt and reliable detection of acute intracranial hemorrhage (ICH) is critical to treatment of a number of neurological disorders. Cone-beam CT (CBCT) systems are potentially suitable for detecting ICH (contrast 40-80 HU, size down to 1 mm) at the point of care but face major challenges in image quality requirements. Statistical reconstruction demonstrates improved noise-resolution tradeoffs in CBCT head imaging, but its capability in improving image quality with respect to the task of ICH detection remains to be fully investigated. Moreover, statistical reconstruction typically exhibits nonuniform spatial resolution and noise characteristics, leading to spatially varying detectability of ICH for a conventional penalty. In this work, we propose a spatially varying penalty design that maximizes detectability of ICH at each location throughout the image. We leverage theoretical analysis of spatial resolution and noise for a penalized weighted least-squares (PWLS) estimator, and employ a task-based imaging performance descriptor in terms of detectability index using a nonprewhitening observer model. Performance prediction was validated using a 3D anthropomorphic head phantom. The proposed penalty achieved superior detectability throughout the head and improved detectability in regions adjacent to the skull base by ~10% compared to a conventional uniform penalty. PWLS reconstruction with the proposed penalty demonstrated excellent visualization of simulated ICH in different regions of the head and provides further support for development of dedicated CBCT head scanning at the point-of-care in the neuro ICU and OR.