Cruise ships are just as stable as any other vessel of their size - And meet the minimum stability criteria set out in SOLAS/class regs.
Most of the machinery (bar AC stations, lifts and the likes) is usually contained within the first 3 decks above the keel, so it's mostly underwater.
The weight of the pools is only a minor issue in the grand scheme of things. That said, the FSM the pools create is often a bigger problem, which is why they're drained during "heavy" weather if possible - Or, at the very least, emptied into a holding tank much lower down.