Although Large Language Models (LLMs) have achieved remarkable success in Machine Translation (MT), a significant performance gap persists between high-resource and low-resource languages due to imbalanced pre-training data. In this paper, we first investigate the internal mechanisms driving this performance disparity from a layer-wise perspective.We propose a metric termed Activation Disparity (𝛥 R) to quantify the activation divergence between high- and low-resource MT. Based on this metric, we distinguish between Task-Adaptive Layers (TAL, 𝛥 R > 0) that encode task-specific signals and Legacy-Inert Layers (LIL, 𝛥 R < 0) dominated by pre-trained bias. Leveraging this finding, we propose the Layer-aware Dual-directional Modulation (LaDM). Integrated with Low-Rank Adaptation (LoRA), LaDM employs a sparse strategy to bidirectionally modulate optimization dynamics. Specifically, it amplifies contributions from TAL to accelerate feature consolidation while inhibiting LIL to dampen misaligned legacy biases. Extensive experiments on Chinese-to-seven low-resource language translation using Llama-3.1, Qwen2.5, and Gemma-2 demonstrate that LaDM significantly outperforms standard LoRA fine-tuning, achieving an average improvement of 1.73 spBLEU.Code is available at https://github.com/zzssqqq/LaDM.