I have shotgunned a fat zombie 3 times to the head, and stabbed it around 40 times when I ran out of shotgun shells on level 10 and it didn't die.
I do wonder if the fat zombies have health regen or not. Cause I have pumped a few hundred rounds of pistol / smgs into on before and it just kept on troopering like nothing happened.
How to defeat a fatso?
First, forget about pistols and SMGs—they won't hurt him at all, and you'll still need the bullets.
Second, leave your knife in its sheath and forget about melee combat altogether—your blows are as bad as a massage for a fatso.
Third, Mr. Shotgun and Mr. Explosives are your most reliable allies in the fight against fatsoes, as they deal damage. But the shotgun is especially good—it's easier to get your hands on and ammo is more common. Let the bastard get close and shoot him right in the face. If it doesn't kill him outright, it'll stun him, giving you time for a second shot or an escape. And, of course, make sure your gun is upgraded.
Fourth, there are exploding gas cylinders on level 12. Lure a fat guy to them and shoot the cylinder. These bastards don't like colorful fireworks, especially when a big gas cylinder explodes right next to them.
As for health regeneration, he's probably just a tough son of a bitch.
In a pinch, you can just run away. Luckily, fat assholes aren't that common.