tip the scales
tip the scales {v. phr.}, {informal}
1. To weigh.
Martin tips the scales at 180 pounds.
2. or tip the balance
To have important or decisive influence; make a decision go for or against you; decide.
John's vote tipped the scales in our favor, and we won the election.
Compare: TURN THE TIDE.
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Source: A Dictionary of American Idioms