We can understand the reason considering the body of the fat person in two parts - Legs up to waist as one part and rest of the body as the second part. (See diagram below).
Center of the mass of the first part is at A (Somewhere near the knees) and the center of the mass of the second part is at B (Somewhere near the chest). So the center of mass of the whole body is at C on the line AB. The total weight of the fat person acts at C and the Normal force by the ground on his body (Which is also equal to W) acts opposite to the weight at his toes T. Though both weight and the Normal force are equal and opposite, their lines of action are not the same. Their lines of action are parallel having some distance d between them. So these antiparallel forces produce a torque equal to W*d on the fat person (Which is clockwise in the figure), and he generally falls.
