The phrase "to support this hypothesis" means that there are reasons or evidence that make it more likely that the idea or theory being proposed is true or accurate. Full definition
The research doesn't support this hypothesis of extreme behavior in the majority of users. (personalfitnessadvantage.com)
Their meta - analyses did not support the hypothesis of sex - differences in attachment. (link.springer.com)
Their results support the hypothesis that the quality of the fat consumed in the diet is important for the development of allergic diseases in children. (healingdaily.com)