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As one of the prevailing deep neural networks compression techniques, layer-wise mixed-precision quantization (MPQ) strikes a better balance between accuracy and efficiency than uniform quantization schemes. However, existing MPQ strategies either lack hardware awareness or incur huge computation costs, limiting their deployment at the edge. Additionally, researchers usually make a one-time decision between post-training quantization (PTQ) and quantization-aware training (QAT) based on the quantized bit-width or hardware requirements. In this paper, we propose the tight integration of versatile MPQ inference units supporting INT2-INT8 and INT16 precisions, which feature a hierarchical multiplier architecture, into a RISC-V processor pipeline through micro-architecture and Instruction Set Architecture (ISA) co-design. Synthesized with a 14nm technology, the design delivers a speedup of $15.50\times$15.50× to $47.67\times$47.67× over the baseline RV64IMA core when running a single convolution layer kernel and achieves up to 2.86 GOPS performance. This work also achieves an energy efficiency at 20.51 TOPS/W, which not only exceeds contemporary state-of-the-art MPQ hardware solutions at the edge, but also marks a significant advancement in the field. We also propose a novel MPQ search algorithm that incorporates both hardware awareness and training necessity. The algorithm samples layer-wise sensitivities using a set of newly proposed metrics and runs a heuristics search. Evaluation results show that this search algorithm achieves $2.2\%\sim 6.7\%$2.2%∼6.7% higher inference accuracy under similar hardware constraints compared to state-of-the-art MPQ strategies. Furthermore we expand the search space using a dynamic programming (DP) strategy to perform search with more fine-grained accuracy intervals and support multi-dimensional search. This further improves the inference accuracy by over $1.3\%$1.3% compared to a greedy-based search.