Endometrial cancer: This is the most likely diagnosis given the patient's postmenopausal status, constant heavy vaginal bleeding, and an enlarged uterus on pelvic examination. Endometrial cancer is a common cause of postmenopausal bleeding, and the patient's obesity (BMI 37.4) is a significant risk factor.

Leiomyoma of the uterus: Uterine fibroids can cause vaginal bleeding and uterine enlargement, even in postmenopausal women. However, they are less likely to cause constant heavy bleeding.
Atrophy of the vaginal mucosa and endometrium: Thinning and friability of the vaginal mucosa, as noted on examination, can lead to bleeding, especially in the context of decreased estrogen levels post-menopause.

Uterine sarcoma: Although rare, uterine sarcomas can present with vaginal bleeding and uterine enlargement, similar to endometrial cancer. Missing this diagnosis could have severe consequences due to its aggressive nature.
Cervical cancer: Although no cervical abnormalities were noted, cervical cancer can cause postmenopausal bleeding. It's essential to ensure that a thorough evaluation, including potential biopsy or further imaging, is considered to rule out this possibility.

Endometriosis: This condition is unlikely in a postmenopausal woman, especially without a history of symptoms during her reproductive years. However, it could be considered if other diagnoses are ruled out and symptoms persist.
Pelvic organ prolapse: While this condition can cause a sensation of heaviness or pressure, it is less likely to cause significant vaginal bleeding. It might be considered if there were symptoms or signs suggestive of prolapse, which are not prominently featured in this case.