Wiktionary
tip the scale
vb. 1 (context idiomatic intransitive English) To change the fortunes, either positively or negatively. 2 (context idiomatic intransitive used with "at" English) To weigh (have a certain weight).
Usage examples of "tip the scale".
It could be something as simple and nontech as primitive ability that's going to tip the scale in this war.
And that we cannot do with our Marines and seamen: but three or four hundred soldiers from Rodriguez would just tip the scale, I do believe.
But it might be just the coin to tip the scale, the straw to light the fire.
Did he imagine that open battle might tip the scale and turn Andrys into an enemy he couldn't defeat?