In recent years, the use of artificial intelligence on resource-constrained IoT devices has grown significantly. However, existing approaches to DNN partitioning and offloading across the edge-cloud continuum typically rely on static methods that ignore runtime dynamics. Furthermore, they are often evaluated in simulated environments rather than on real hardware. To address this gap, we propose a framework that dynamically splits neural network layers across the heterogeneous continuum. The framework profiles the model at startup, measures network link conditions between nodes, and periodically re-evaluates the partition to adapt to environmental changes. We created a physical testbed comprising a Raspberry Pi edge device, a laptop fog, and a high-performance desktop PC as the cloud. We evaluated the framework over three widely adopted convolutional neural networks: VGG16, AlexNet, and MobileNetV2. Our results show that the framework achieves reductions in energy and end-to-end latency of 27.09--35.82% and 6.34--22.92%, respectively, compared to a static partitioning baseline. These findings confirm the superiority of adaptive to static partitioning.