Why half empty bottle is more stable than full one?

full bottles are top heavy. half full one's are not.

The above answer is only true if the bottle is shaped so there is more water in the top half then the bottom half when full. Otherwise the bottle is not top heavy. It is just as heavy (or sometimes only slightly less heavy) on top as it is on bottom. Where as a half empty bottle has a heavier base to keep it from toppling over easier. The same principle is used in the engineering of skyscrapers. The foundation goes deep into the ground and weighs many times the weight of the top so it will not fall because of a windy day.