The Hall-plateau width and the activation energy were measured in the bilayer quantum Hall state at filling factor u=2, 1 and 2/3, by changing the total electron density and the density ratio in the two quantum wells. Their behavior are remarkably different from one to another. The u=1 state is found stable over all measured range of the density difference, while the u=2/3$ state is stable only around the balanced point. The u=2 state, on the other hand, shows a phase transition between these two types of the states as the electron density is changed.