Stroke recovery requires intensive and continuous rehabilitation over a long period of time. Access to existing rehabilitation devices is limited to hospitals due to the considerable cost and maintenance. This paper proposes a lightweight, low-cost gravity-balanced exoskeleton for home rehabilitation of upper limbs. Gravity balancing is based on a two-bar mechanism that can fit the periphery of a human arm. A type of planar flexural spring is proposed to achieve the required spring potential energy. This type of spring has a thin cross-section and can be designed and fabricated conveniently. A model is constructed to optimize the geometry and dimension of the exoskeleton. Performance is evaluated through a static analysis. The results show that the proposed exoskeleton is both simpler and lighter than existing passive devices. It can be easily custom-made for different arm masses and sizes. We expect the exoskeleton to be used in both clinical and homecare environments for the arm rehabilitation of stroke patients.