Low-dimensional representations are increasingly used to study meaningful organizational principles within the human brain. Most notably, the sensorimotor-association axis consistently explains the most variance in the human connectome as its so-called principal gradient, suggesting that it represents a fundamental organizational principle. While recent work indicates these low dimensional representations are relatively robust, they are limited by modeling only certain aspects of the functional connectivity structure. To date, the majority of studies have restricted these approaches to the strongest connections in the brain, treating weaker or negative connections as noise despite evidence of meaningful structure among them. The present work examines connectivity gradients of the human connectome across a full range of connectivity strengths and explores the implications for outcomes of individual differences, identifying potential dependencies on thresholds and opportunities to improve prediction tasks. Interestingly, the sensorimotor-association axis emerged as the principal gradient of the human connectome across the entire range of connectivity levels. Moreover, the principal gradient of connections at intermediate strengths encoded individual differences, better followed individual-specific anatomical features, and was also more predictive of intelligence. Taken together, our results add to evidence of the sensorimotorassociation axis as a fundamental principle of the brain's functional organization, since it is evident even in the connectivity structure of more lenient connectivity thresholds. These more loosely coupled connections further appear to contain valuable and potentially important information that could be used to improve our understanding of individual differences, diagnosis, and the prediction of treatment outcomes.