Ok first of all you really need to learn more about your condition. As you have no thyroid now, you have Hypothyroidism. I also have this, but due to Hashimoto's rather than cancer. Managing it is a lifelong issue and it can be a long and difficult adjustment to get the meds/dosage correct.
125mg Levothyroxine really isn't that high, your consultant is wrong. Many people take up to 200 or even more. TSH stands for "thyroid stimulating hormone" and it is your body telling you how much thyroid hormone you need. It determines how much levothyroxine they give you. However this is a very controversial subject because many doctors believe levothyroxine alone is enough, or don't give the correct amounts etc.
Basically your thyroid naturally creates two hormones - T4 and T3. Once you have Hypothyroidism your body doesn't create enough, so you replace it with Levothyroxine. However, Levothyroxine contains T4 only. The idea is your body should convert some of that T4 into T3. For a lot of people this works. But many people find this doesn't happen and they continue to have symptoms despite being on Levo (such as weight gain).
Some doctors will prescribe T3 alongside Levo which for many people helps a lot. I personally take something called NDT (previous posters have mentioned this too) which is a natural alternative which contains T4 and T3. I have to get it privately though as the NHS doesnt prescribe it. Basically the NHS is absolutely shite at managing thyroid conditions. They give you Levothyroxine, and send you on your way. If you keep having symptoms (like I did) they tell you you're depressed 🙄🙄
I would highly recommend checking out the HealthUnlocked Thyroid UK forum. Full of extremely knowledgeable people who will advise you. Your life isn't over! You can sort this out. You may have to go private to do so, but there are things you can do.
I personally lost no weight on Levo, but since being on NDT have lost 4kg without changing my diet whatsoever.
Highly recommend learning as much as you can about hypothyroidism. The more you know, the more chance you have of getting your health back.