They take one hit but one that does 2 damage. A more powerful hit than those that do damage 1. Hits don't add up, so two weak damage1 results don't equate to a damage2 effect.
You'll see on the weapon cards the last entry is the amount of damage each weapon does. A Shotgun would blast a fatty away as it does Damage2.
You might feel an itch to add up lower damage results into fewer powerful results. This should be resisted. That variety of damage output in the weapons, and fatties soaking up damage is a really rather important thing in providing variety. Would be a nightmare to track how many wounds any given zombie has too.
Abominations are even more severe. They require a damage3 hit, or the old molotov cocktail.