Throwing weight around means to use one's power or influence to assert dominance or control over others. The antonyms of this phrase include humility, meekness, and modesty. Humility means having a modest or low view of one's importance, which entails being respectful and considerate towards others. Meekness involves exhibiting patience and gentleness, rather than aggression or arrogance. Modesty is characterized by a lack of pretension, a willingness to listen to others, and a desire to serve rather than dominate. These opposing concepts serve as a counter to the negative connotations of throwing weight around, creating an environment of cooperation and mutual respect.