Vision-Language-Action (VLA) models enable instruction-following robotic manipulation, but they are typically pretrained on 2D data and lack 3D spatial understanding. An effective approach is representation alignment, where a strong vision foundation model is used to guide a 2D VLA model. However, existing methods usually apply supervision at only a single layer, failing to fully exploit the rich information distributed across depth; meanwhile, naïve multi-layer alignment can cause gradient interference. We introduce ROCKET, a residual-oriented multi-layer representation alignment framework that formulates multi-layer alignment as aligning one residual stream to another. Concretely, ROCKET employs a shared projector to align multiple layers of the VLA backbone with multiple layers of a powerful 3D vision foundation model via a layer-invariant mapping, which reduces gradient conflicts. We provide both theoretical justification and empirical analyses showing that a shared projector is sufficient and outperforms prior designs, and further propose a Matryoshka-style sparse activation scheme for the shared projector to balance multiple alignment losses. Our experiments show that, combined with a training-free layer selection strategy, ROCKET requires only about 4% of the compute budget while achieving 98.5% state-of-the-art success rate on LIBERO. We further demonstrate the superior performance of ROCKET across LIBERO-Plus and RoboTwin, as well as multiple VLA models. The code and model weights can be found at https://github.com/CASE-Lab-UMD/ROCKET-VLA.