Stroke: The combination of homonymous hemianopsia, unilateral weakness, and headache strongly suggests a stroke, particularly one involving the posterior circulation or a large vessel occlusion in the anterior circulation. The visual field defect and weakness are consistent with a lesion in the brain that affects both the optic tract and the motor pathways.

Brain Tumor: A tumor in the brain, especially in the parietal or temporal lobe, could cause homonymous hemianopsia by affecting the optic radiation and unilateral weakness by involving the motor cortex or its descending pathways. Headache could be due to increased intracranial pressure.
Arteriovenous Malformation (AVM): An AVM could cause these symptoms by bleeding, which leads to increased intracranial pressure (headache), or by its mass effect on surrounding brain tissue, affecting vision and motor strength.

Pituitary Apoplexy: Although less common, pituitary apoplexy is a medical emergency that can present with sudden headache, visual field defects (including homonymous hemianopsia if the optic chiasm is involved), and potentially weakness if there is associated increased intracranial pressure or involvement of surrounding structures.
Subarachnoid Hemorrhage: This condition, often due to aneurysmal rupture, can cause sudden severe headache and, depending on the location and extent of the hemorrhage, could lead to visual field defects and focal neurological deficits like unilateral weakness.

Mitochondrial Encephalomyopathy, Lactic Acidosis, and Stroke-like episodes (MELAS): A rare genetic disorder that can cause stroke-like episodes, including visual field defects and weakness, along with headache. It is more common in younger patients.
Cerebral Vasculitis: Inflammation of the blood vessels in the brain can lead to a variety of symptoms, including stroke-like episodes, headache, and visual disturbances. It is a rare condition that requires a high index of suspicion for diagnosis.