Accurate segmentation of the left atrial (LA) wall in 3D late gadolinium-enhanced MRI (LGE-MRI) is essential for wall thickness mapping and fibrosis quantification, yet it remains challenging due to the wall's thin geometry, complex anatomy, and low contrast. We propose C2W-Tune, a two-stage cavity-to-wall transfer framework that leverages a high-accuracy LA cavity model as an anatomical prior to improve thin-wall delineation. Using a 3D U-Net with a ResNeXt encoder and instance normalization, Stage 1 pre-trains the network to segment the LA cavity, learning robust atrial representations. Stage 2 transfers these weights and adapts the network to LA wall segmentation using a progressive layer-unfreezing schedule to preserve cavity features while enabling wall-specific refinement. On the 2018 LA Segmentation Challenge dataset, C2W-Tune outperformed an architecture-matched baseline trained from scratch. The wall Dice score increased from 0.623 to 0.814, surface Dice at 1 mm increased from 0.553 to 0.731, 95th-percentile Hausdorff distance (HD95) decreased from 2.95 mm to 2.55 mm, and average symmetric surface distance (ASSD) decreased from 0.71 mm to 0.63 mm. Under reduced supervision using 70 training volumes sampled from the same training set, C2W-Tune achieved a Dice of 0.78, remaining competitive with recent multi-class bi-atrial benchmarks, typically 0.6-0.7. These results show that anatomically grounded task transfer with controlled fine-tuning improves accuracy for thin LA wall segmentation in 3D LGE-MRI.