The size of the Supreme court is not defined in the Constitution. So, packing the court is not unconstitutional. It is dishonest and shady as hell. But, the only check on the power of each branch are the other two branches that don't desire to be sidelined by one branch growing more powerful. All three branches are supposed to be in contention for power within the bounds of their interpretation of the Constitution. It is the duty of the other two branches to deem an action of the third branch as unconstitutional.

But, the system has been broken over time. Congress abdicated the majority of their power to the executive and somehow judicial became the official arbiters of constitutionality.