Prior work has attempted to understand the internal structures and functionalities of Transformer-based encoder-decoder architectures on the level of multi-head attention and feed-forward sublayers. Interpretations have focused on the encoder and decoder, along with the combinatorial possibilities of the self-attention, cross-attention, and feed-forward sublayers. However, without examining the low-level structures, one gains limited understanding of the motivation behind sublayer reordering. Could we dive into the sublayer abstraction and permute layer weight matrices to improve the quality of translation? We propose AEIUOrder to greedily reorder layer weight matrices in the encoder by their well-trainedness, as measured by Heavy-Tailed Self-Regularization (HT-SR) metrics, and order the decoder matrices correspondingly. Our results suggest that greedily reordering layer weight matrices to maximize Total well-trainedness facilitates the model to learn representations and generate translations more effectively.