In summary ...

Force is a measure of the interaction between bodies, mass is a measure of the amount of material in an object, weight is the gravitational force acting on a body (although for trading purposes it is taken to mean the same as mass) and load usually means the force exerted on a surface or body.

In detail ...

Force

Force is a measure of the interaction between bodies. It takes a number of forms including short-range atomic forces, electromagnetic, and gravitational forces. Force is a vector quantity, with both direction and magnitude. If the forces acting on a body in equilibrium are summed around the periphery of the body they add to zero. If there is any resultant force acting the body is not in equilibrium and it will accelerate such that the rate of change of the body's momentum (velocity × mass) is equal and opposite to the force. If the body is held stationary in some way, then there will be a reaction acting on the body from the support structure that is equal in magnitude and opposite in direction to the force imposed. Although the definition of force units is based on acceleration of a free body, most force measurements are made on bodies in equilibrium, and are therefore measures of forces within a structure. Conceptually a structure can be 'cut' across any section and the forces acting within the body at that section are those which would act at the free surfaces if such a cut were made. This property is the basis of most force measurements - a physical support or link in a structure is replaced with a device that measures the forces acting at that point.

As with any vector quantity, the force and reaction may be projected onto three orthogonal axes, and the equilibrium may be considered independently parallel to each of those axes. Frequently a force measurement system will react properly only to forces along its principal axis, and if this should not coincide exactly with the direction of the total applied force to be measured then an erroneous result will be generated.

The SI unit of force is the newton (N); defined as the force which would give to a mass of one kilogram an acceleration of one metre per second, per second. It is not convenient, in practice, to produce an acceleration of one metre per second, per second acting on a mass of one kilogram in order to realise a standard of force of one newton. Instead the practical realisation of the unit of force makes use of known masses, which when subjected to the effect of local gravitational force, exert a known force on an earth located support. The mechanical structure to handle and control such masses is known as a deadweight machine.

Mass

Mass is a measure of the amount of material in an object, being directly related to the number and type of atoms present in the object. Mass does not change with position, movement or alteration of a body's shape unless material is added or removed. The unit of mass in the SI system is the kilogram (kg) which is defined to be equal to the mass of the international prototype kilogram mass held at the International Bureau of Weights and Measures (BIPM). Mass is also the inertial resistance to acceleration.

Weight

In the trading of goods, weight is taken to mean the same as mass, and is measured in kilograms. Scientifically however, it is normal to state that the weight of a body is the gravitational force acting on it and hence it should be measured in newtons, and this force depends on the local acceleration due to gravity. To add to the confusion, a weight (or weightpiece) is a calibrated mass normally made from a dense metal, and weighing is generally defined as a process for determining the mass of an object.

So, unfortunately, weight has three meanings and care should always be taken to appreciate which one is meant in a particular context.

Load

Load is a term frequently used in engineering to mean the force exerted on a surface or body.