Thank you for your suggestions. Boy, fighting weight gain is not easy.
Diet and exercise is critical with both hypothyroid and diabetes for good weight management/ weight loss.
You can head across to the thyroid forum for some more info on making sure your levels are optimal.
Your HA1C is not so high, so I'd guess they'd have started you on metformin. This drug often helps with weight loss. Regardless, you won't gain if you pay close attention to diet. Reduce the carbs, particularly anything processed and refined. Don't eat too much fruit. Get a blood sugar monitor and test regularly. Before breakfast in the morning and 2 hours after start of eating. This will let you see the effects of different foods on your blood sugar and help you tailor what you eat.
It depends on the medication. Metformin, the most commonly prescribed type 2 medication does help with weight loss. But mostly you need to cut carbs (good for blood sugar management anyway), reduce fat and increase exercise. Also make sure your thyroid is stable as that of course affects weight as well. Congratulations on your A1C!