tip the scale(s)
To upset the balance of a situation, such that one side or element is favored or gains advantage. The two candidates are so close in the polls that both are vying for something that will tip the scale in their favor. The immense interconnectivity of social media has tipped the scales of power somewhat back into the hands of the ordinary population.
tip (or turn) the scales (or balance)
(of a circumstance or event) be the deciding factor; make the critical difference. tip the scales
1. To register weight (at a certain amount).
2. To offset the balance of a situation.