When your metabolism isn't working, you gain weight. The hypothyroid issues (whether caused by AF or the original problem) slows the whole system down.
Also, as a woman you can gain lots of water weight from imbalanced hormones. AF can cause water retention when it is not yet at the Addison's level, too. That you said "bloated" is telling...it can be an entirely different feeling from just weight gain.
Dr. Lam's OAT Axis article is a great read.
I read on Mary Shonom's (sp?) thyroid site on About.com a survey of hypothyroid people and what diets or methods helped them lose weight. Atkin's was hand's down the winner. But, it causes issues w/ AF because of drastic carb cuttine...Schwarzbein talks about the fact that metabolizing protein in the absence of carbs requires your adrenals to produce adrenaline.