Acceleration Due To Gravity When Finding The Weight Of An Object $W=mg$
When finding the weight of an object, why do we multiply the mass of the object by the acceleration do to gravity $g$ even though the object isn't moving downwards?
 A: Actually, to find the force (weight) you are multiplying the mass by the local gravitational field. 
The reason people colloquially say 'acceleration due to gravity' is because of Newton's 2nd law, applied to the gravitational force. If the local gravitational field is designated by $\vec{g}$, then the force is
$$\vec{F}_g=m\vec{g}.$$
According to Newton's 2nd Law, the acceleration of an object is proportional to the applied force with a proportionality constant, $1/m$. So we can write
$$\vec{a}=\frac{1}{m}\vec{F} = \frac{m\vec{g}}{m}=\vec{g}.$$
We see from this that the acceleration due to the gravitational force is the same vector as the gravitational field, $\vec{g}$.
If you want to calculate the contribution of a radially-uniform spherical planet to the local gravitational field, neglecting rotational effects and free-fall reference frames, the field magnitude would be
$$g=\frac{GM_p}{r^2},$$
where $G$ is the universal gravitational constant, $M_p$ is the mass of a spherical planet (inside the distance $r$), and $r$ is the distance to the center of the planet.
A: The weight of an object is typically thought of when putting something on a scale. But where does the force come from that pulls an object downward in the first place? It is the force of gravity acting on the object. And from Newtown's second law, we know that a net force has the relation: $F_{net}=ma$. Sometimes for gravity calculations we simplify it to $W=mg$ because it is implied that it is the force of gravity on an object, and the g is the acceleration due to Earth, or whatever body an object is on (Moon, Mars, etc). So it isn't actually moving downward, but the calculation allows us to see how much it is being pulled downward. 
A: The weight of an object is given by $W = mg$. But how do you measure the weight? You measure it by using a machine, like a spring balance or a weighing machine. When we keep the object on the machine, it exerts a force on the platform or spring (in case of spring balance). There is also a reaction force (or tension in case of spring balance). This force is equal and opposite. So, the object doesn't move.
Consider the example below. Suppose a block of mass $m$, rest on a weighing platform.

In this case, the force $N$ is the normal reaction force provided by the platform. As the object doesn't move, so $N = mg$. The reading which is shown by the machine is this value, which is $N$.
So even if the object doesn't move, that doesn't mean there are no forces. It means that there is no net force. Thus, the weight of an object is mass times $g$, even if it is not moving as the reading scale reads the $N$.
