The body does not fight to hold onto weight. Sorry, that is wrong. If that was the case there would not be any underweight anorexics. Also look up the Minnesota starving experiment and biosphere 2. Both experiments found that there was no clear evidence of the metabolism slowing down. It might have happened to a very small degree, it might have been statistical noise.
I did read a paper a while ago (sorry, not in English) that being hypothyroid slows down the energy your body needs by not more than 4% of the base metabolic rate. Say you weight 75kg, you're a 170cm large female, around 45 years old. Your BMR then is around 1469kcal. 4% of this is 59kcal. That means, you'd need to eat 59kcal less per day to prevent you from gaining weight. Or if you continue to eat as before you will gain about 6kg before your energy intake and energy expenditure is in balance again.
The reason why you gain weight is mainly from:
waterweight: if your hypo your body hold onto more water. With the right dose of levo you'll lose this water weight again.
being less active: The BMR is the energy your body uses when you were in a coma. On top of that is all the activity energy. If you're hypo you tend to have less energy to do things, but keep on eating the same you gain weight
being more hungry: being hypo can make you more hungry, and portion size creep will lead to weight gain.
being frustrated from being less active, feeling miserable and gaining weight: some people compensate by eating more.
Thus using hormones can help with weight loss, but mainly by shedding water weight and making you feel better and more active again. It does not speed up metabolism again.
Note: I lost 40lbs while having untreated hashimoto. It's just about eating less food than your body needs. Yes, it requires commitment and precise logging, which you might not have if you feel not well. But that's what you need to do. Now I actually need to take care that I don't lose more weight as I'm much more active and the levo makes sure I'm less hungry. I certainly cannot afford to lose more weight.