The damage is dealt by the same source as the original source of damage. The doubled damage isn’t dealt by Calamity Bearer unless it was the original source of damage.

If another effect (or effects) modifies how much damage your Giant source would deal—by preventing some of it, for example—the player being dealt damage or the controller of the permanent being dealt damage chooses the order in which any such effects (including Calamity Bearer’s) apply. If all of the damage is prevented, Calamity Bearer’s effect no longer applies.

If damage dealt by a Giant source you control is being divided or assigned among multiple permanents and/or players, that damage is divided or assigned before doubling. For example, if you attack with a 5/5 Giant with trample and it’s blocked by a 2/2 creature, you can assign 2 damage to the blocker and 3 damage to the defending player. Those amounts are then doubled to 4 and 6, respectively.