I don't want to get too far off from the OP's question. Everyone has a unique body so what works for one person may not work for another. Some people get super into counting calories, those being consumed and those burned (though, interestingly, rarely those going out), and that's great if it's working for them. Other's, like myself, don't count anything and eat as much as they want of high quality, whole foods and have stable appropriate weights. Before anyone jumps on genetics as a reason, yes genetics can affect a person's tendencies but possibly a lot less than people think. For myself, my older blood relatives are almost all overweight/obese/diabetic. Plus there is mounting evidence that epigenetics plays a huge role in metabolic processes. What one eats, and other lifestyle factors, determines what genes are switched on or off and thus what one's genetic expression is.
I wanted to post my advice because it is contrary to a lot of what people are told and it's important that people know that there are a multiple schools of thought (and thanks to AnanonymousGuy for doing the same). For the OP, I would advise not repeating what hasn't worked in the past and try something new. There's no better choice you can make in life than to invest in your health and support your loved ones in doing the same.
Now because I know my advice may sound somewhat odd I want to respond to some of the criticisms, hopefully without anyone feeling attacked or offended. My views are based on the best research I have come across, if anyone has views that differ it doesn't mean that we need to frame things as right/wrong. The human body is incredibly complex and there is so much we still do not know. The truth may ultimately incorporate a lot of people's different views but explain the contexts under which they are true.
Organic vegetables have no magical fat burning properties
Actually, I find that organic vegetables do have calorie burning qualities, and it's not magic, it's just chemistry. Many people in the US don't eat enough vegetables (though to be fair, vegetables are also largely grown in nutrient depleted soils) and thus are deprived of several nutrients needed to metabolize the rest of the food they're eating. Diets high in refined foods tend to deplete magnesium and chromium, among others. Both of these minerals are critical in processing sugars/carbohydrates. Lack of magnesium has been shown to increase insulin resistance; supplementing with magnesium has been shown to increase insulin sensitivity. Thus a diet high in magnesium rich vegetables (like leafy greens) given to a depleted individual will facilitate more glucose moving into the cells and being used for energy instead of being converted into fat (ie, increased metabolism).
I would say not butter or oil so much as avocados or a fatty fish like salmon.
Salmon and avocados are both great foods to be eating. So is the much-maligned butter. By eating butter from pasture-raised, hormone-free, antibiotic-free cows you get: all of the fat soluble vitamins (A, D3, E, K1, K2), healthy fats (lauric acid, conjugated linoleic acid, omega-3's, medium-chain triglycerides), and some minerals.
Which ever demons caused the weight to begin with, will ultimately win unless they're dealt with, first. That's not the fault of calories or any diet in particular... that's the fault of our society as a whole teaching us to treat symptoms and not the root of the problem.
We are absolutely in agreement that society focuses on treating symptoms and not the root of the problem. But then how does one know if the root is physiological or psychological (assuming those are even a useful distinction for treatment)? You might be surprised how many psychological demons (for example, bulimia and other obsessive food thoughts) can be vanquished with some 5-HTP.
Which brings me back to my original point. In this country people overwhelmingly believe that people are fat because they're lazy when in reality they may be lazy because they're fat. For the OP, it sounds like his wife has a brain that's in a starvation state thus putting on excessive weight from meals and not being interested in exercise. Also, based on the symptoms provided I suspect his wife has chronically low serotonin levels. I would predict for this individual that calorie restriction will be problematic, as will getting her to exercise more than just a little bit. But no one has to take my word for it...
Anyway, now I'm off to the gym. My apologies for the lengthy post.