Case 1: sum of the rest < Biggest
We are putting all the objects in two points in a single line that goes through the centre, heaviest one at a point and the others at the opposite. if you don't put them in the same place the vectors will only divert the centre of gravity outside of the line and the concentration of those vectors at the opposite point will be lesser. So the centre of gravity will travel more towards the heavy object which will only worsen our result.
Case 2: sum of the rest >= Biggest
We are calculating the concentration of mass at the opposite point of the heavy object. As the sum is more, we need to reduce some mass. By changing the angle of an object we can do that easily thus reaching equal concentration of the heaviest object. So the centre of gravity will be at the centre.
