How do we calculate an objects weight?

The calculation would basically depend on what you already know.


1) "In the physical sciences, the weight of an object is the magnitude, W, of the force that must be applied to an object in order to support it (i.e. hold it at rest) in a gravitational field. The weight of an object in static equilibrium equals the magnitude of the gravitational force acting on the object, less the effect of its buoyancy in any fluid in which it might be immersed.
Near the surface of the Earth, the acceleration due to gravity is approximately constant; this means that an object's weight near the surface of the Earth is roughly proportional to its mass."
Source and further information:
http://en.wikipedia.org/wiki/Weight

(the last sentence applies only if buoyancy does not play a big role)


2) In most cases, buoyancy does not have a big influence and you just have to calculate the gravitational pull.

The weight is then:
P = m g
where
m is the mass of the object
g the local value of the acceleration due to gravity

"Nevertheless, the Earth's gravitational field can vary by as much as 0.5% at different locations on Earth (see Earth's gravity). These variations alter the relationship between weight and mass, and must be taken into account in high precision weight measurements that are intended to indirectly measure mass. To eliminate this variation, when the weight of objects is used in commerce, the value given is what the objects would weigh at a nominal standard gravitational acceleration of 9.80665 m/s2"
Source and further information:
http://en.wikipedia.org/wiki/Weight

For this calculation, you would have to know the mass of the object and the local value of gravity.
On Earth, you could take an approximation, for instance:
g ~ 9.81 m/s^2

Please notice that you could calculate the mass if you know the volume and the density:
m = V d
where
V is the volume
d is the density


3) The last calculation is useful if you have to take buoyancy into account.
For a solid in water, buoyancy is the weight of the displaced volume of water.

B = mb g = Vb db g
where
mb is the mass of displaced volume of water,
Vb is the displaced volume of water,
db = 1 kg/dm^3 is the density of water
(this in the case where the fluid is water)


4) Further information:
- "How to Calculate the Weight of Steel":
http://www.ehow.com/how_5127389_calculate-weight-steel.html
- "How to Calculate Weight Using Density & Volume":
http://www.ehow.com/how_4965287_calculate-weight-using-density-volume.html
- "How do scientists measure or calculate the weight of a planet?":
http://www.scientificamerican.com/article.cfm?id=how-do-scientists-measure
- "Using Math To Calculate Your Weight In Outer Space":
http://www.mathmotivation.com/science/gravity.html

The weight of an object depends on its mass and the gravitational field strength:
weight = mass x gravitational field strength
The units for these quantities are as follows:
Weight is measured in newtons (N).
Mass is measured in kilograms (kg).
Gravitational field strength is measured in newtons per kilogram (N/kg).
The gravitational field strength depends on the force of gravity. On Earth it is 10 N/kg, but it varies depending on planet size.
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examville.com

Measure it's volume and then id it's weight per unit volume