Generally, the pitch becomes lower. It is much easier to speak lower as you become fatigued by the excess weight. Breathing becomes harder, so you work harder for breath suppotr-and at the wrong pitch. Though being overweight can induce a voice problem, or add to it, the weight need not cause or contribute to voice difficulty. It depends upon the individual, the circumstances, and how the voice is used.
Weight is but one factor that affects the voice.
I have been told that posture is the reason I have a bad voice. Posture has very little to do with voice production. The way you move your head, stand, or sit, is of little importance in the correct use of your voice. If you have a bad voice, it is due to incorrect pitch, tone focus, volume, quality, and breathing. My voice seems to be worse with a change in the weather.