What keeps these huge cruise ships from tipping over when they get into high seas and storms?
Their center of gravity and buoyancy is still set in the water. To picture that see this: https://www.youtube.com/watch?v=a79yUWofnSY
Ballast (weight deep in the ship).
There is a lot of weight below decks to balance the ship. besides the ship is wider than you think to avoid that top heavy feeling.
They call it Equilibrium, or in science of hydraulic Engineer as ,Buoyancy ,since there is stabilizer at the bow of the ships and by using Force Plate Balance to keep its stable or in equilibrium all the time , especially during the high seas and storms.