Probably the only advantage in keeping the uterus is that it requires more surgery to remove it.
All your hormones come from the ovaries, so you'll have a big drop in hormones after removing the ovaries, and uterus has nothing to do with that.
A big advantage to removing the uterus is that it makes hormone replacement significantly easier. It's then only necessary to replace estrogen. If the uterus is in place, it's necessary to also replace progesterone to protect the uterine lining.
Removing the uterus means that you won't get uterine or cervical cancer or pre-cancer.
Bladder incontinence usually has little or nothing to do with the uterus. If you have a dropped uterus (prolapse), it can drag the bladder down and be a cause of incontinence.
Any weight gain after the surgery may be related to hormone loss or inactivity, but not from whether the uterus is present or not.
Sexual function usually has little to do with the uterus. Some women get sexual pleasure from pressure on the cervix, but most women have equally good sex after the uterus is removed. If your estrogen is low after surgery, that can cause problems sexually.
So I think that he main issue is that it's more surgery to remove the uterus than to just remove the ovaries. For most women it's probably better to remove the uterus as well. Best wishes.