Weight gain isn’t listed among Suboxone’s known side effects.
Researchers have found that some people in early recovery do gain weight, usually due to other factors such as better nutrition once they discontinue using drugs.
People with opioid use disorder often gain weight in early recovery. Studies suggest that this weight gain is not due to Suboxone, but more likely other changes in lifestyle associated with early recovery. 
More than 3,000 people using Suboxone have participated in side effect research. While many experienced side effects like constipation and insomnia, no weight gain was reported. The U.S. Food and Drug Association (FDA) does not associate Suboxone with any appreciable weight gain. 
But you may gain weight in early recovery. Frequently, this is due to eating habits.
Individuals misusing opioids may have been malnourished in the setting of chronic drug use. When they enter recovery, they may start eating more regularly, causing them to gain weight.  In these cases, weight gain is probably a good thing as it indicates a return to proper nutrition.
In other instances, individuals may substitute one bad habit with another (although arguably less dangerous) habit of junk food instead of drugs. In this case, weight gain might also be expected. 
Of note, Rates of obesity are similar in patients on Methadone for OUD and the general population.
If you're worried about your weight, talk with your doctor. A healthy diet and exercise could help.
If you notice that you’re substituting food for drugs (which is easy to do, especially in early recovery), talk with your treatment team. Addressing this problem in therapy early could help avoid developing poor coping mechanisms as you make this significant life change.