Background Explanations for the evolution of female-biased, extreme Sexual Size Dimorphism (SSD), which has puzzled researchers since Darwin, are still controversial. Here we propose an extension of the Gravity Hypothesis (i.e., the GH, which postulates a climbing advantage for small males) that in conjunction with the fecundity hypothesis appears to have the most general power to explain the evolution of SSD in spiders so far. In this "Bridging GH" we propose that bridging locomotion (i.e., walking upside-down under own-made silk bridges) may be behind the evolution of extreme SSD. A biomechanical model shows that there is a physical constraint for large spiders to bridge. This should lead to a trade-off between other traits and dispersal in which bridging would favor smaller sizes and other selective forces (e.g. fecundity selection in females) would favor larger sizes. If bridging allows faster dispersal, small males would have a selective advantage by enjoying more mating opportunities. We predicted that both large males and females would show a lower propensity to bridge, and that SSD would be negatively correlated with sexual dimorphism in bridging propensity. To test these hypotheses we experimentally induced bridging in males and females of 13 species of spiders belonging to the two clades in which bridging locomotion has evolved independently and in which most of the cases of extreme SSD in spiders are found. Results We found that 1) as the degree of SSD increased and females became larger, females tended to bridge less relative to males, and that 2) smaller males and females show a higher propensity to bridge. Conclusions Physical constraints make bridging inefficient for large spiders. Thus, in species where bridging is a very common mode of locomotion, small males, by being more efficient at bridging, will be competitively superior and enjoy more mating opportunities. This "Bridging GH" helps to solve the controversial question of what keeps males small and also contributes to explain the wide range of SSD in spiders, as those spider species in which extreme SSD has not evolved but still live in tall vegetation, do not use bridging locomotion to disperse.