What was its purpose and in which part of the aircraft was it being used?
The counterweights were 12 to 83lbs, 99% depleted uranium, coated with nickel and cadmium. There were "21 to 31" of the weights in the tail, with 692-1059 pounds of counterweights per plane. It was used on planes from 1968-1981, Boeing estimates about 300 tons in use (or as spares).
They switched to tungsten counterweights after that.
Boeing noted the location in the tail meant the depleted uranium was 25 feet from the back of the passenger cabin, and about the same distance to ground personnel.
simpleflying says there were six weights in (each) elevator and eight in the rudder.
sources: 1994 letter from Boeing to Oak Ridge National Laboratory (pdf), simpleflying.
Depleted uranium was used as counterweights at the aileron balance panels; the outboard elevator and the upper rudder. Counterweights are used for maintaining the center of gravity(CG).
The process of maintaining CG falls under weight and balance. All proceedings and measures are found in the type certificate data sheet(TCDS) and it also includes the maximum certificate take off weight(MCTOW)
The CG must be always situated forward of the center of pressure(COP)
"You might have seen the flight crew moving person(s) from their seats to another seat after each stop overs" That is a part of the weight and balance procedure.
The idea behind this procedure is to NOT make the nose heavy as just condition will require additional runway distance during T/O and also increase the stall speed while a Tail heavy condition will make it harder to level the flight after T/O and would cause a wing stalling.
Stall speed is the minimum velocity at which the wings can begin to produce lift
Wing stall occurs when the transition point A.K.A boundary layer moves forward towards the leading edge of the wing during a high rate of climb and/or when the boundary layer is shortened. Transitional point is a point on the wings upper chamber at which the laminar flow of the relative wind breaks and changes to turbulent flow and its effect reduces lift
So what was the reason?
Uranium was ideal because of its high density property such as a small volume unit can have a greater amount of mass and occupy less space yet still provide the needed weight to counter balance the aircraft
This depleted uranium was cladded with nickel and cadmium and painted with a primer and a topcoat. However, the risk of human exposure to this radioactive material was extremely high especially in the maintenance side of things. Therefore, changes were being made with the introduction of Tungsten.
Cladding is a procedure that involves coating a metal with a thin layer of another metal. Either to minimise corrosion or with bearings you would do this procedure to harden its surface while keeping its core ductile/and or soft