Spiders are the most sexually size dimorphic terrestrial animals and the evolution of this dimorphism is controversial. Patterns of sexual size dimorphism (SSD) in spiders have been related to individual performance and size. In 2002 Moya-Laraño, Halaj & Wise proposed the 'gravity hypothesis' to explain patterns of sexual size dimorphism in spiders whereby species building webs high in the vegetation are predicted to show greater SSD than those that build lower down. They advocated an advantage in climbing speed in smaller males searching for females in high places. The gravity hypothesis predicts a negative relationship between male size and climbing speed. In 2007 Brandt & Andrade questioned this interpretation and proposed that the pattern of SSD in spiders is better explained by an advantage for larger males of low-dwelling species to run faster along the ground. We induced male spiders to run a standard distance up vertical poles of different diameters to examine the predicted relationship between size and climbing speed. We tested two species of extremely size-dimorphic orb-web spiders, Argiope keyserlingi and Nephila plumipes, that differ in the height at which females tend to build webs, and one species of jumping spider, Jacksonoides queenslandica, with low levels of size dimorphism. We also examined morphological determinants of horizontal motility by inducing males to run along a raceway. Substrate diameter was consistently found to influence climbing performance. In N. plumipes, climbing speed was slowest on the widest diameter substrate. In A. keyserlingi, size-adjusted leg length and substrate diameter interacted to determine climbing speed, while in J. queenslandica, there was an interaction between body size and substrate diameter on climbing speed. In the effect of substrate diameter, we have identified a potential bias in previous tests of the gravity hypothesis. Our results do not support the prediction of the gravity hypothesis. There was no evidence of a negative relationship between body size and climbing speed in the two orb-web species with high levels of SSD. Our results are also not consistent with a recent modification of the gravity hypothesis that suggests a curvilinear relationship between climbing speed and size. Body size was positively associated with maximum running speed only in the cursorial hunter J. queenslandica. For this spider, results are more consistent with Brandt & Andrade's explanation for variation in SSD in spiders, that larger males are selected for superior running ability in low-dwelling species, rather than selection for smaller size for climbing to females in high-dwelling species.