How much weight will I gain when I lose my thyroid due to surgery?

No change. You should not gain or lose weight with thyroid surgery. You should be placed on thyroid replacement right after surgery. If the dose is correct, there should be no change in your thyroid level and thus no effect in weight loss/gain. A blood test 2-3 months after starting thyroid replacement will tell you if the dose chosen was the correct dose.
None. If you are started on thyroid hormone replacement right after surgery, you should have no symptoms of hypothyroidism at all.