Not every person who is hypothyroid is fat or gained weight quickly. The opposite is true for hyperthyroid people--not all of them are skinny. Most of hypo people are hypo because of an autoimmune disorder--Hashimito's. Weight gain, if applicable, is not the only symptom. Other symptoms can include: edema, fatigue, anemia, body aches and pains, depression, etc. In order to be diagnosed, the doctor has to take a history of the patient's symptoms and order a thyroid panel for blood work.
Since hypothyroidism is most often autoimmune, hypos often have other AI conditions (i.e. celiac intolerance, allergies). Not all, but some do. For some, they also have other disorders like diabetes, PCOS, Insulin Resistance, etc. For them, cutting out processed carbs might work and improve their conditions. What works for one person is not a cure-all for all other hypos.
Additionally, weight gain is caused primarily because a hypo's metabolism has decreased. The thryoid is responsible for a lot of body processes, including metabolism. If your thyroid is off, your metabolism is gonna be off, too.
I don't know what sites you found but the sites I have seen pretty much advocated cutting out processed carbs. Maybe you should look up Mary Shomon.
I know a lot more about the thyroid than about the adrenals (just mostly that they deal with stress).
EDIT: I forgot to mention a few things:
1. treatment--for most hypos, they need medication (i.e. levothyroxine, cytomel, synthroid). A few hypos are able to forgo medication and change something about their lifestyle that does help them. A lot of hypos also can be prescribed Armour (naturally made from pig or cow thyroid while the others that I mentioned are synthetic).
2. Some women do become hypo after a pregnancy, and most of the time, it is temporary. For those that don't improve at some point will have to continue with treatment.