Why do low ballast tanks improve cruise-ship stability?

Answer: Lowering the ship's center of gravity

Lowering the ship's center of gravity ✓ — Right. Putting water low in ballast tanks lowers KG, the height of the ship's center of gravity above the keel. Since GM is roughly KM minus KG, lowering KG gives more initial stability if free-surface effects are controlled. The hidden twist is that ballast is not just dead weight; its vertical position is the whole point.

Using sloshing water — No. Free liquid sloshing is usually a stability penalty, not the trick that keeps the ship steady. A half-full tank can shift its mass toward the low side and reduce GM. The useful ballast condition is controlled low mass, often with tanks full or empty enough to avoid a large free-surface effect.

Adding simple weight — Close, because ballast does add weight, but the same weight can help or hurt depending on height. If you put mass high, it raises KG and makes the ship less stable. Low ballast works because of placement, not because extra kilograms are automatically good.