Many women do gain weight after a hysterectomy.
More Info: Studies suggest that weight gain following a hysterectomy is dependent upon what type of procedure is performed. If the ovaries remain intact, then there is little affect on weight, whereas if the ovaries are removed, triggering menopause, then weight gain may be a side effect as with any menopausal woman.
Not All Hysterectomies Result in Weight Gain
Research has indicated that long-term weight gain after hysterectomy appears to be limited to only those that require a bilateral oophorectomy, a procedure that removes the ovaries, triggering menopause to set in immediately.  These findings are not surprising because menopause, whether natural of surgically induced, can contribute to weight gain.
The Effects of Estrogen Deficiency on Weight Gain
During menopause, and a year or so following menopause, estrogen levels begin to decline. Research has indicated that estrogen assists in weight maintenance by regulating hunger and energy expenditure.  An estrogen deficiency may also lower metabolic rate as well as contribute to insulin resistance in turn increasing fat storage. 
Effects of Ovary Removal during Hysterectomy
Weight gain is not the only concern for those having ovaries removed during a hysterectomy. It is estimated that half of all hysterectomy procedures include the removal of the ovaries and that many are performed as a preventative measure to reduce cancer risk. These numbers are beginning to raise controversy as several studies have indicated that the benefits of the removal may not outweigh the risks involved in some cases. A study conducted by John Hopkins oncologists and epidemiologists concluded that ovary removal in women younger than forty-five is strongly associated with arthritis and bone thinning in later years. Another study conducted at St. John’s Health Center concluded that while ovary removal does decrease the risk of cancer, the procedure increases the risk of coronary heart disease, lung cancer, and death overall. 
Weight Gain Following Hysterectomy- Short Term
There are several reasons that any type of hysterectomy procedure may cause short-term weight gain. If you have an abdominal hysterectomy, it can take up to eight weeks to fully recover from the surgery. During this period, many women are far less active than they are before their surgeries, but few women take their reduced activity into consideration when it comes to their post-surgical diet. While some women lose weight during the first week after surgery due to normal post-surgical loss of appetite, most begin gaining weight after that. An extra 500 calories per day that would normally be expended through activity can lead to a one-pound weight gain per week. Because most women have hysterectomies at an age when their metabolisms have already begun to slow, it can be particularly hard to lose the weight they pick up after their hysterectomies. 
 International Journal of Obesity, Gibson, CJ
Body mass index following natural menopause and hysterectomy with and without bilateral oophorectomy.
2012, Volume: 164, print
 UT Southwestern Medical Center
Study Shows Estrogen Works in the Brain to Keep Weight in Check
Menopause, Weight Gain, and Exercise Tips
 John Hopkins Medicine
Ovary Removal in Younger Women Linked to Bone Thinning and Arthritis
 Obstetrics & Gynecology, Parker, William
Ovarian Conservation at the Time of Hysterectomy and Long-Term Health Outcomes in the Nurses’ Health Study
2009, Volume: 113, No: 5
 US Department of Health and Human Services Office of Women’s Health
Hysterectomy Fact Sheet
Glossary of Terms
Oophorectomy: a surgical procedure to remove one or both of your ovaries.
Insulin resistance: Insulin resistance is a condition in which the cells of the body become resistant to the hormone insulin.
“For the last 35 years, most doctors have been routinely advising women undergoing hysterectomy to have their ovaries removed to prevent ovarian cancer. We believe that such an automatic recommendation is no longer warranted.”
William H. Parker M.D. New Study Finds Removing Ovaries during Hysterectomy Increases Risk of Death, Outweighs Benefits, Medical News Today