Very nice article. I believe, according to the National Weight Registry, it's something like 15-20% of people have been able to take off 10% or more of their weight, and keep it off for more than 5 years.
Anecdotal: in 2003 I took off 14% of my weight, kept it off since. Tried everything (keto included, folks) to get it just a bit lower, nothing worked - except - yes, more exercise. Now 18% less than in 2003.
My sense from reviewing the research is it's very different for different people. Dr. Ludwig is very good on this, as he tends to support lo carb but also recommends whole grains (low glycemic), and legumes for those who do well on them, as well as a much wider variety of fruit than the lo carb people usually recommend.
As far as whether exercise works, if someone just says "move more" obviously it's not scientific.
Almost everyone who reads these articles knows strength training and HIIT (2-3x a week max) are good. A lot of conflicts about cardio - latest I saw, and this has been my experience over not just 18 years but over many decades - is long moderate cardio (at least 45') DOES help. Maybe not with you, maybe not with most people, but I've had too many experiences where I've kept my diet the same and after gaining a few extra pounds, did nothing different but do moderate jogging for an hour every day and the extra weight just melted off.
It's incredibly simple, folks. Take a look at Dr. Ludwig's page. It's basically a modified Meditarranean diet,the most researched diet in the world. The Harvard nutrition chart (which Ludwig approves of) is a great guide.
They have excellent exercise research on the Harvard site as well. It's not an accident their nutrition department is considered #1 among more than 15,000.