I have seen divers in colder water load as much as 40 pounds on a weight belt when wearing a 6 mm two-piece wetsuit. If this weight is not well distributed, it can cause problems with buoyancy and balance at depth, as well as significant back and hip discomfort. Also, the problems caused by a too-tight BC can be compounded when it must be inflated to compensate for the increased amount of lead and loss of buoyancy at depth. Obese divers also tend to consume more air than other divers because of the greater effort required to move through the water. This is particularly true if there is a current.
Currents can lead to even faster air consumption, a dangerous situation for overweight divers.
Being out of shape is a factor in increased air consumption, too. Obese people are at an increased risk of heart attack and subsequent drowning while diving. However, fitness is probably less of a factor than the obesity itself. Nitrogen, the gas most responsible for causing DCS, is five times more soluble in fat than in muscle tissue. This means that an overweight diver will absorb more nitrogen than a leaner diver for any given time and depth.