It’s not true that if you are overweight that your voice pitch is low. The vocal fold is composed of soft tissues, therefore if the vocal cord gets heavy and the voice does become low it is due to the tissues having more fat.
However, please know that body type does not relate to the voice’s ability. A lot of great singers who are obese can extend or contract the vocal cord easily, and have varied ranges of pitch.
The above reasons pertaining to the the amount of soft/light and hard/heavier tissues are factors of determining voice pitch.
The condition of voice changes in association with the body type, but the voice pitch depends on a lot of individual factors.
Note1: Swollen vocal cords are also a reason to cause the voice to be low. This is because the space is narrowed between the thyroid cartilage and the hyoid bone, which obstructs blood circulation.