Bluetooth Low Energy (BLE) is currently the dominating wireless network solution for eHealth and sports. However, most BLE sensors require dedicated applications with limited development capabilities. This paper presents a method for rapid development of applications in distributed BLE IoT systems for eHealth and sports. The method is implemented as a JavaScript web framework based on HTML5 canvas, WebSocket and Web Bluetooth APIs. This paper demonstrates how the framework can be applied to develop an application for monitoring physical activity and heart rate. The framework enables software and service operators to iteratively create, tune and deploy filter algorithms in distributed BLE IoT systems, without rebooting nodes or restarting programs using dynamic software updating.