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Climate signatures recorded in the geometry of branching streams provide insight into climate and landscape histories on Earth and other planetary bodies. Recent findings establish that branching angles are narrower and stream profiles are straighter in more arid climates. However, these two observations have been attributed to different mechanisms. Here we demonstrate that for US watersheds the difference in slope between confluent streams increases with humidity, and streams with a greater difference in slope tend to branch at wider angles. Our observations suggest a branching angle endmember of 90° when stream slopes are most different. Using a simple model of runoff erosion, we show how this variation in relative stream slopes can be explained by a shift in streamflow accumulation across climate regimes. These findings connect previously observed climate signatures in branching angles and stream profiles, suggesting that both record the same control of aridity on surface flow.