Tip the balance/scales
Definition 1 of 3
Pro Tip 1/3Outcome Oriented
Focus on how 'tip the balance' means changing a result or decision. 
Her passionate speech might just tip the balance in her favor at the debate.
Pro Tip 2/3Subtle Change
Understand that it doesn't require a big influence to tip the balance, sometimes a small detail is enough. 
A slight cost reduction could tip the balance for consumers choosing between similar products.
Pro Tip 3/3Figurative Shift
Recognize that 'tip the balance' is often used figuratively to describe influencing factors. 
The unexpected support from the community tipped the balance for the local team.