throw one\'s weight around

1. The force with which an object near the Earth or another celestial body is attracted toward the center of the body by gravity. An object's weight depends on its mass and the strength of the gravitational pull. The weight of an object in an aircraft flying at high altitude is less than its weight at sea level, since the strength of gravity decreases with increasing distance from the Earth's surface. The SI unit of weight is the newton, though units of mass such as grams or kilograms are used more informally to denote the weight of some mass, understood as the force acting on it in a gravitational field with a strength of one G. The pound is also still used as a unit of weight.

2. A system of such measures, such as avoirdupois weight or troy weight.

Our Living Language  : Although most hand-held calculators can translate pounds into kilograms, an absolute conversion factor between these two units is not technically sound. A pound is a unit of force, and a kilogram is a unit of mass. When the unit pound is used to indicate the force that a gravitational field exerts on a mass, the pound is a unit of weight. Mistaking weight for mass is tantamount to confusing the electric charges on two objects with the forces of attraction (or repulsion) between them. Like charge, the mass of an object is an intrinsic property of that object: electrons have a unique mass, protons have a unique mass, and some particles, such as photons, have no mass. Weight, on the other hand, is a force due to the gravitational attraction between two bodies. For example, one's weight on the Moon is ¹/₆ of one's weight on Earth. Nevertheless, one's mass on the Moon is identical to one's mass on Earth. The reason that hand-held calculators can translate between units of weight and units of mass is that the majority of us use calculators on the planet Earth at sea level, where the conversion factor is constant for all practical purposes.

throw (one's) weight around definition

1. tv.
   to show off one's importance or power; to use one's rank or station to advantage. : The vice president was throwing his weight around, but that had little effect on anything.