Will treating my obesity lower my risk of cancer?

I have struggled with obesity since I was in my late teens (I am now 36). There's a history of cancer in my family, especially uterine, ovarian, and breast cancer on my mother’s side. I’ve heard that being overweight can increase a person’s risk of getting cancer after menopause. My question is, wouldn’t it be logical that if I deal with my weight issues now, then I’ll be lowering my chances of getting cancer later in life? I’m really worried about this, and I’d be so grateful if someone could answer this, and perhaps explain it a little better to me. Thank you very much.