Everything close to the Earth experiences the force of gravity close to the Earth. This force is called the weight of the object.
If the object is free to move it will accelerate down because of the force of the Earth's gravity acting on it. If an object is not free to move however – if for example, it is on a table – the force of gravity does not vanish. It is there, and has the same magnitude and direction as if the table were not there. The object will experience the force of gravity but remain stationary relative to the Earth, so there must be a force equality and opposite to the force of gravity acting on the object.
This equal and opposite force is called the reaction force, labelled R above. The origin of the force is a bit more complicated. It arises from repulsive forces between the electrons in the atoms of each surface.
Of course, a table cannot exert a reaction force to balance ANY weight. If the weight is too heavy the table will not be able to support it and will break, but for any lesser weight the reaction force will be equal to the weight.