Is resistance training an important part of a weight management routine?

It can. Exercising large areas of muscles like the glutes promotes higher return in caloric burning as well as better structural support for surrounding bones and tissues.
Yes. Resistance training builds lean muscle tissue and that is what burns calories. Without lean muscle tissue you will have a hard time keeping the weight off. Add some form of resistance training to your workouts 2 days or more a week.
Sometimes. . Resistance training may reduce weight in some patients, while some individuals may gain weight. The only way you can tell with your body is take daily pre and post training weight checks.