It makes absolutely no practical difference, actually.
All objects are accelerated at the same rate by gravity. On Earth resistance from the air makes a difference (why a feather and a bowling fall at different rates), but the effect of air resistance between a fat person and a thin person is going to be negligible to the point of being unmeasurably small.
Someone brought up the idea of having more kinetic energy with more mass, but while true, it's not particularly relevant. What kills people in impacts is not the overall force applied to their body as a whole, (F=ma) it is the blunt force to specific parts of your body (your brain smashing into your skull rapidly, your heart being crushed by the impact of the ground, blood vessels and arteries breaking open, etc.). Whether you're fat or thin, your head is going to decelerate at the same rate and cause the same damage to your brain when you hit the ground, etc. If anything, the fact that fat absorbs and (to some degree) dissipates impact forces, means that having lots of fat would have a protective effect in impact traumas (the opposite of what you'd expect from just using "F=ma"), but it's not a significant effect. You smash into concrete at over 150 kph (as you will from a 30 story free fall), you're just dead, no matter how fat or thin you are.