In this work, we present SkinnyPower, a technology for Intra-Body Power Transfer (IBPT) that wirelessly transfers power through human skin to operate batteryless wearable sensors. We envision a scenario, in which batteryless sensors placed on small body parts (e.g., on-finger, in-ear, and in-mouth) can obtain operating power from another body-worn energy sources (e.g., already existing battery-powered wearable devices such as a smartwatch or a BandAid-like battery patch attached to the neck). The key technical challenges in realizing this vision include 1) providing a robust return path in the body channel - where the forward (power signal) and return (ground) paths are not explicitly defined - using implicit capacitances formed between the devices and earth ground, and 2) achieving reliable operation despite variations in capacitive coupling between the skin and devices, devices and earth ground, and conductance of the subdermal layer. We identify and optimize critical system design parameters to maximize the power transfer between a transmitter and a receiver with the capacitively coupled return path. To demonstrate and validate the concept of IBPT, we implemented a prototype consisting of 1) a wrist-worn, battery-equipped power transmitter that sends alternating current through the human body and 2) a finger-worn, batteryless sensor device that operates solely on body-transferred power. Evaluations on five subjects show that we can reliably support the power of approximately 1 mW, which can be used to operate an embedded system, continuously collect sensor (e.g. accelerometer) data, and wirelessly transfer the collected data in real-time using Bluetooth Low Energy. Moreover, we achieve a power transfer rate of 14.5% between the transmitter and receiver, which is significantly higher than other wireless power transfer techniques such as RFID. We believe that the proposed system has great potential to transform current architectures and designs for body-area networks, promoting the development of innovative on-body sensors that would otherwise not be possible with on-device batteries.