While it’s unlikely you could drink enough heavy water to really harm yourself, the hydrogen bonds formed by deuterium are stronger than those formed by protium. One critical system affected by this change is mitosis, the cellular division used by the body to repair and multiply cells. Too much heavy water in cells disrupts the ability of mitotic spindles to equally separate dividing cells .
Theoretically, you’d have to replace 20 to 50% of the regular hydrogen in your body with deuterium to experience symptoms ranging from distressing to catastrophic. For mammals, replacing 20% of the body’s water with heavy water is survivable (although not recommended); 25% causes sterilization, and about 50% replacement is lethal.2
Since only about one water molecule in 20 million naturally contains deuterium—which adds up to about five grams of natural heavy water in your body and is harmless—you don’t really need to worry about heavy water poisoning. Even if you did drink some heavy water, you’d still be getting regular water from food.