Basically hypothyroidism in the uk is mainly autoimmune (antibodies attack thyroid), other causes are surgery linked, iodine deficiency (unlikely here) and very rarely a pituitary problem. Or you are born without one. I think there can be a viral link too but it might be also linked to the autoimmune bit (not sure on this) As the treatment is effectively the same they don't often test for antibodies unless the thyroid levels have been hovering at borderline - as antibodies would indicate that it's going to deteriorate. If not I'm guessing it might high light another issue in a borderline case.
But you're diagnosed hypo so probably do have antibodies, and it's worth being aware that sometimes autoimmune issues go hand in hand eg pernicious anaemia (auto immune issue where you can't absorb b12)
So really good to get a full blood test screen, you could try cutting out gluten; my mil was told she was not coeliac but was gluten intolerant and quite unwell (though had had lots of weight loss and pale stools).
I'm hashimotos I guess as antibodies; but 100% well IF Tsh kept around 1 or just below, and recently, if ferritin very good. And vit d and b12, as I had all these tests. Gluten makes no difference (sugar does though), but that's just me. I also had Addisons test, muscle enzyme tests, esr the works - it literally boiled down to correct thyroxine dose and boosting iron, and I was really quite unwell until this was corrected.
I agree 75 mg doesn't seem much. With no thyroid (harder to know if it's all been destroyed yet) it's weight linked. However for post menopausal women they do keep thyroxine a little lower due to osteo issues.
The Tsh range is 0.3 to about 4.5; you should be aiming for the lower end. Most people only feel well below 2. It's not nice guidelines as yet here for general hypo, but it IS the nice guideline if you're trying to conceive; it states Tsh should be below 2 or 2.5 to conceive.
In order to fine tune Tsh it's possible to take a 25 every other day; I take 125/150 alternate days. 125 is too low, 150 too high. It's worth remembering this if gp suggests raising then wants to lower.