What condition presents with proximal muscle weakness and a rash on the eyelids?

The condition characterized by proximal muscle weakness accompanied by a rash on the eyelids is dermatomyositis. This autoimmune disorder primarily affects the muscles and skin, leading to the hallmark symptom of muscle weakness, particularly in the proximal muscles such as those in the hips, shoulders, and back. The associated skin manifestations can include heliotrope rash, which is a violaceous rash located on the eyelids, as well as the presence of Gottron's papules, which appear as erythematous or violaceous papules over the dorsal surfaces of the joints.

This combination of muscle weakness and distinctive skin rashes is key in diagnosing dermatomyositis, setting it apart from other conditions like multiple sclerosis, which focuses more on neurological symptoms, and polymyalgia rheumatica, which generally presents with muscle pain and stiffness rather than weakness. Lupus erythematosus can cause a variety of rashes and systemic symptoms, but the specific combination of proximal muscle weakness and that particular eyelid rash aligns closely with dermatomyositis. Hence, the features and clinical presentation directly link this condition to the symptoms described in the question.