Again, only hypotheses at this time, but the existing data is far from fluffy and there’s a lot more in the pipes.
The most compelling research I’ve seen used various semi-controlled diets (unfortunately diet was indicated but ultimately self reported by subjects, as it didn’t occur strictly in a controlled environment) with some subjects receiving fecal transplants. Those receiving diverse flora from transplants succeeded much better in losing weight and keeping it off some months later. The study needed stricter controls and more subjects, but it’s a fascinating start.
I’ll point out that the cause of the differences in results isn’t necessarily gut flora alone, too — it’s all super preliminary. This comment is mostly just to say “there are other factors, we just aren’t sure what yet but we have some interesting leads”.
I still managed to lose 40 pounds via calorie restriction and absolutely no change in exercise.
I basically did strict keto for 6 months. CICO is a real thing. Even hypothyroid, you're not going to gain weight if you aren't intaking the calories.