The thrifty gene hypothesis (TGH) is one of the most pervasive ideas surrounding obesity. It suggests that humans have historically lived in alternating periods of feast and famine. So those with thrifty genes, which promote food seeking behaviours, efficiency in using calories and the storage of excess calories to fat, were better able to survive periods of famine and reproduce. Therefore in the modern environment with access to unlimited food and no need for physical activity those of us who have thrifty genes are the ones that get fat.
The TGH was originally used to explain how the Pima have higher rates of obesity/T2D. The TGH suggests that because the Pima have been living a traditional lifestyle up until more recently than those of European descent, therefore the Pima have been subject to feast and famine for longer and so more of them would have the thrifty genes that produce obesity in a perpetually food abundant environment .
The TGH is based on several key premises that aren’t supported:
Humans have historically lived in alternating periods of feast and famine: Pacific islanders such as the Nauruans (the most obese and diabetic nation) and Hawaiians are particularly vulnerable to obesity and T2D when they adopt a western diet and lifestyle, leading people to believe these people carry more of the thrifty gene. However, Pacific islanders live in a tropical climate and generally have an abundance of food year round (the Kitavans are a perfect example of this: “It is obvious from our investigations that lack of food is an unknown concept, and that the surplus of fruits and vegetables regularly rots or is eaten by dogs.”), and previously there were no reports of obesity/T2D among them*, which is true of other hunter-gatherers as well. Thrifty genes should actually be more common in those of European descent because of European winters and famine being more a feature of early agriculture with a heavy reliance on harvest time and on a small number of crops. Something like the Irish potato famine just simply would not happen to hunter-gatherers  .
Famines apply a selection pressure that favours thrifty genes: During periods of famine, infectious disease and plant toxins kill more people than starvation. This is likely due to micronutrient deficiencies and hunger driving people to eat rotten or poisonous food. Also, famines mostly affect the mortality rates of the young (<5) and the old (>60), the wrong demographics for a selection pressure. The old are past their reproductive years and childhood obesity is very recent 
. Also, it has been calculated that if thrifty genes conferred a very modest survival advantage, then almost everyone would would have thrifty genes, therefore it's unlikely that thrifty genes conferred any positive selection pressure 
In our modern environment those with thrifty genes will overeat, get fat and stay fat because the famine never comes: If this were true then people with thrifty genes (those who are or will become overweight/obese) would gain weight and not be able to lose weight on ad libitum diets, but this is not the case. Obese Hawaiians lost weight on an ad libitum diet of traditional foods  (probably high in fruit, starchy vegetables and fish). People on low carb or low fat diets done ad libitum spontaneously reduce calories and outperform calorie restricted diets for weight loss 
Therefore the overweight/obese likely have thrifty genes: Evidence actually suggests pre-obese people don't have a lower metabolic rate . Many people with obesity actually use calories much less efficiently. They tend to have low numbers of mitochondria and a slow, inefficient electron transport chain , which when coupled with higher numbers of glycolytic enzymes and lower numbers of aerobic enzymes, increases the wasteful process of fermenting glucose and excreting of lactic acid . They tend to have more fast-twitch muscle fibres , which use energy less efficiently than the slow-twitch muscle fibres .
How does thrifty genes and overweight/obesity convey any advantage when having higher body fat:
- Requires more energy at rest and to move
- Makes one slower and less athletic
- Produces more pro-inflammatory cytokines and other cellular signalling (such as low adiponectin) that promotes poor health and disease 
- Probably reduces sexual selection
An alternative explanation as to why the Pima/islanders/etc have higher rates of obesity is their lack of adaptation to new foods which may include alcohol, milk, fruit (fructose malabsorption), seeds, refined sugar and nutrient poor foods. (The list depends entirely on the traditional culture) and other factors like poverty.
The TGH is often used to justify weight loss approaches. CICOs can use it to say we get fat because of too much feast and to lose weight we need to replicate famine (calorie restriction). Low (fatters/carbers/fructosers) can use it to say (fat/carbs/fructose) was a scarce resource found only in the warmer months** so the (dietary fat/insulin from carbs/IR>LR from fructose) increases body fat and locks the fat from (fat/carbs/fructose) into adipocytes until winter.
* Some people use the Venus figurines as evidence that hunter-gatherers regularly experienced obesity (during times of plenty). But I think it is more likely that ancient artists recreated the extraordinary - the people the figurines were modelled from had rare genetic mutations such as the ob/ob gene.
** Many of these theories assume European seasonality, whereas the tropics – where humans originally came from – experience much different seasonality.
*** The Thrifty Phenotype Hypothesis (TPH) is very different to the TGH. The TPH suggests famine and a scarcity of nutrients (low birth weight) or T2D mothers delivering excess amino acids and glucose (high birth weight) to the baby in utero compromises normal metabolism and predisposes them to later T2D . The effect of the TPH is interesting, but it’s a long way from being a major factor in T2D or obesity
**** It’s surprising that something so entrenched in the public mindset as the thrifty gene hypothesis attracts so little attention in academia. Searching for ‘thrifty gene’ on PubMed gives me 51 free studies, ‘thrifty gene hypothesis’ only 20, but searching for ‘type 2 diabetes mitochondrial dysfunction’ gives me 252