Smoking is associated with a low prevalence of thyroid antibodies. Withdrawal enhances thyroid antibody levels and may be a risk factor for the development of hypothyroidism. The risk of an overt autoimmune hypothyroidism diagnosis is more than a 6 fold increase in the first 2 years after cessation of smoking.
I think smoking cessation and weight gain sort of "automatically" go together, just like hypothyroidism and weight gain go together. I quit smoking about 6 years ago and was diagnosed with hypo a year later, though I'm pretty sure I was hypo for a good while before being diagnosed.
You may be cutting your calories by too much. You need a certain amount of calories, just to live - to maintain bodily functions: heart, lung, brain, liver, kidney function, etc. If you don't take in enough calories, your metabolism will slow down even more to conserve fat stores. You need to figure out how many calories you need for basic functions, then drop approximately 500 calories/day from that. You can also expend some of those calories via exercise.
If the only test your doctor is doing is TSH, he's doing you a great disservice. Without the FT3 and FT4 tests, you have no idea whether your levels are actually "right" for you or not. TSH does not correlate with symptoms; FT3 does.
You should also ask to get tested for thyroid antibodies, Thyroid Peroxidase Antibodies (TPOab) and Thyroglobulin Antibodies (TGab) to determine whether or not you have Hashimoto's Thyroiditis. With Hashimoto's, the body sees the thyroid as foreign and produces antibodies to destroy it. The destruction process usually lasts for several years, but doesn't have to. As the antibodies destroy more and more thyroid tissue, the thyroid produces less and less hormones. This causes a need for periodic adjustments of medication. Once there is no more healthy thyroid tissue, levels often stabilize and the need for adjustment declines.
Try to get the FT3, FT4 and antibody tests. If you doctor refuses, you should start looking for another, because this one will keep you ill.