Document-level relation extraction (DocRE) aims to extract relations between entities from unstructured document text. Compared to sentence-level relation extraction, it requires more complex semantic understanding from a broader text context. Currently, some studies are utilizing logical rules within evidence sentences to enhance the performance of DocRE. However, in the data without provided evidence sentences, researchers often obtain a list of evidence sentences for the entire document through evidence retrieval (ER). Therefore, DocRE suffers from two challenges: firstly, the relevance between evidence and entity pairs is weak; secondly, there is insufficient extraction of complex cross-relations between long-distance multi-entities. To overcome these challenges, we propose GEGA, a novel model for DocRE. The model leverages graph neural networks to construct multiple weight matrices, guiding attention allocation to evidence sentences. It also employs multi-scale representation aggregation to enhance ER. Subsequently, we integrate the most efficient evidence information to implement both fully supervised and weakly supervised training processes for the model. We evaluate the GEGA model on three widely used benchmark datasets: DocRED, Re-DocRED, and Revisit-DocRED. The experimental results indicate that our model has achieved comprehensive improvements compared to the existing SOTA model.