Definition:Weight


 * Physics: The weight of a body is the force exerted on it by a gravitational field.


 * Network theory: The weight of an edge or arc of a network is the functional value assigned to that edge or arc by the weight function of that network.


 * Statistics, etc.: A weight function on a set $S$ is a mapping from $S$ to the (usually positive) real numbers.

Natural Language
In natural language, and by extension to the context of statistics and network theory, the weight of an abstract concept equates to its importance.