tip the balance , also: tip the scales
tilt the balance , also: tilt the scales

Because then he'd have a chance to tip the scales in his favor.

This year world population tipped the scales at five billion.

"This was a year when it wouldn't have taken much to tip the scales."

He put on 15 pounds to tip the scales at 220.

He might just be able to tip the scales in our favor.

A very small thing could tip the scales they weighed on.

And do you know what tipped the scales for me?

The winner was the team that tipped the scales first.

"Any one of these recent decisions could tip the scales against him."