As a very general rule, and one that's broken all the time, people tend to lose weight when hyper, maintain when euthyroid (neither hypo nor hyper) and gain weight when hypo.
I think one cause of this is what you stated, "not adjusting their food intake to their progressively lower metabolism". However, I believe that overmedication is probably also a big factor. Finding the right dose of meds for each individual is a process. In that process, people are apt to become hypo. If that happens, ATMs should be lowered. Weight gain or inability to lose weight is a hypo symptoms, so if meds are properly adjusted, it shouldn't be an issue. If you notice hypo symptoms...fatigue and/or drowsiness despite sufficient sleep, cold intolerance, depression, constipation, etc...you should have blood work and see your doctor for a meds adjustment. You have to walk the fine line between hypo and hyper.
Excerpt from the article "Losing Weight with Hypothyroidism"...
"It seems likely that hypothyroidism, with its penchant for slowing down everything else in our systems right down to our cells, slows down our body's ability to process carbohydrates and our cell's ability to absorb blood sugar. Hence, the carbohydrates we could eat pre-thyroid problems now are too much for our systems to handle. So excess carbohydrates equals excess insulin equals excess weight. Plus, the fun side effects of blood sugar swings (tiredness, dizziness, fatigue, exhaustion, hunger, etc.) that we may be mistaking as thyroid symptoms and our doctors say can't possibly be.
Any illness -- such as the chronic thyroid problems we all face -- also creates physical stress. And stress raises cortisol levels. And increased cortisol increases insulin levels. (I know my cortisol was through the roof last time the doctor checked. She had no idea why.) More insulin means increased chance of insulin resistance.
There's also a vicious circle aspect to this. The liver mediates between the activities of the insulin-releasing pancreas and the adrenal and thyroid glands, which are supposed to "tell" the liver to release glucose. If the adrenals and thyroid aren't working properly on the "telling" end, or if the liver is sluggish, stressed out, or toxic, and not working on the "receiving" end, the system goes out of balance. Either way, the result is elevated excess insulin."