The antonyms for "more big-headed" would be humble, modest, unassuming, and self-effacing. These words describe individuals who do not have an inflated sense of their own importance, and who recognize their strengths and limitations. Humility and modesty are positive character traits that are valued in most cultures, as they promote a spirit of cooperation and a willingness to learn and grow. Being self-effacing and unassuming means that individuals are willing to share credit and recognize the contributions of others, rather than taking all the credit for themselves. In short, these antonyms describe individuals who are down-to-earth and easy to work with, making them valued members of any team.