【Influence】 ,  【authority】 ,  【prestige】 ,  【weight】 ,  【credit】  are comparable when they mean power exerted over the minds or acts of others either without apparent effort or as the result of the qualities, the position, or the reputation of the person or thing that exerts this power.

【Influence】 suggests a flowing from one thing into another of something imperceptible or impalpable; this connotation is retained when the word implies the effect or effects which one person or thing insensibly has on another or the ascendancy which one person or thing similarly acquires over another. However  【influence】  often loses this implication of insensible or unconscious operation and suggests instead the conscious use of personal power or, sometimes, of underhanded means to determine the acts of another; in this sense it often follows the verb use or one of its synonyms.

【Authority】 originally was applied to one (as a preacher, teacher, or writer) or to writings or utterances having the power to compel belief or to win acceptance. In such cases the word usually imputed great learning, great wisdom, or divine inspiration to the person or his work.

This sense persists and  【authority】 is still applicable to a person or publication that is able or qualified to gain credence or to inspire belief in its authoritativeness. From this use mainly, but also from its other sense (see POWER 3 ),  【authority】 has come to be applied also to the power resident in a person or thing that is able because of his or its inherent qualities to win the devotion or allegiance of men and to gain rather than exact their obedience and belief.

【Prestige】  , in contrast with  【authority】 , implies the power to gain ascendancy over the minds of men and to command their admiration for distinguished and superior performance, or for conspicuous excellence in its kind.

【Weight】 denotes measurable 【influence】 , especially in determining the acts of others.

【Credit】  (see also BELIEF 1 ) denotes 【influence】 that arises from one’s reputation for inspiring confidence or admiration.