I just need to clarify, you mentioned thyroid, but do you have a thyroid problem and you are being medicated for it???
The weight and hair issue is common for thyroid sufferers. If you have a thyroid problem i'd guess you are hypothyroid? It can take time for weight and hair issues to correct as you have to wait for the meds to start working.
It would be advisable for you to get your Vitamin D and your Ferritin (iron stores) tested, they ought to be up at thigh end of the lab range to be of benefit.
My hair was shedding too much, but now it's better. I still get phases where it sheds more at certain times, but much better than what i was before. My thyroid doctor rechecks my TSH, Free T3, Free T4, Thyroid Antibodies, ACTH, morning cortisol level, ferritin, Vit D, quite regularly while he's trying to stabilise everything. He's also keeping tabs on my adrenal function and estrogen, progesterone, testosterone and DHEA-S during intervals by doing a saliva test, just to see that my hormones are balancing out, as everything was thrown out of balance with me.
A lot goes wrong when the thyroid isn't working properly and it affects so many other areas within the body. If you are being medicated for your thyroid it's a good idea that your doctor checks your adrenal function to see what your cortisol is doing as too much or not enough cortisol can cause hair shedding too. If your cortisol and your DHEA-S are not balanced then that too will cause hair shedding. Low Ferritin or low Vit D can cause hair shedding. Your thyroid T4 and T3 not being where they ought to be can cause hair shedding.
It's better to find out what's wrong and what's not, rather than risking more side effects by using a hair restorative which can potentially cause more problems. Years ago when i first began noticing my abnormal shedding, my GP told me to use Rogaine. I was fortunate that the lady at the chemist laughed and found it ridiculous, saying i was wasting my money and i should find out what my problem was. I didn't know back then that it was thyroid related as i kept being told my thyroid was fine, when it wasn't.
Good luck and hoping things get better for you