The cerebral cortex is made up of roughly six horizontally organized layers with unique cytoarchitectural properties distributed across the cortical mantle. This gradual variation of laminar structure is a fundamental principle of cortical organization. The similarity of regions in their laminar structure, with roots in development, is suggested to relate to the likelihood, strength and direction of their connectivity. Current accounts of laminar structure variation are mainly based on theory-driven approaches in which histological samples of the cortex are labeled into discrete types based on visual inspection of laminar features. Here, leveraging on a data-driven map of the six cortical layers in the BigBrain, we aimed to quantitatively characterize the gradual variation of laminar structure in the cortex. We identified an organizational axis of laminar thickness covariance which differentiated the dominance of infragranular and supragranular layer thickness and in general followed a rostro-caudal trajectory. This axis was co-aligned with the cortical hierarchy such that infragranular-dominant regions towards the rostral pole of the cortex were overall higher up this functional hierarchy. Furthermore, laminar thickness variation was linked to connectivity, with regions with similar laminar thickness showed higher likelihood and strength of connectivity. Laminar thickness covariance was also related to structural covariance, reflecting shared developmental/maturational and genetics effects of the regions with similar laminar structure, which hints at developmental origins of laminar structure variability. In sum, we describe the organization of layer-wise thickness covariation in the cortical mantle and how it relates to structure and function.