気(き)が大(おお)きくなる means to become uninhibited. They become more courageous than normal.

The expression 気が大き means you don’t care about the small things. You’re uninhibited. Adding なる denotes the action of becoming uninhibited.

Examples of 気が大きくなる

Further Reading

• Garrison, Jeff et al. Kodansha’s Dictionary of Basic Japanese Idioms, Kodansha, 2002, p. 233