The majority of people who are overweight have difficulty losing weight. If they didn't there wouldn't be an obesity crisis in the western world.
OBESITY CRISIS: TWO BILLION PEOPLE NOW OVERWEIGHT AND U.S. IS ONE OF THE FATTEST NATIONS ON EARTH source
Doing blood tests on 2 billion people who can't lose weight is almost a complete waste of money and resources.
As regards to a claim of a proper diet most people will tell you that they're on a good diet. And almost always that is incorrect because their knowledge of nutrition is misinformed. Again, if their knowledge were correct they would be less likely to be in this position. To support this at least one study has shown that nutritional knowledge is inversely correlated with healthy eating.
Students with greater nutritional knowledge consumed less unhealthy fats and cholesterol. This finding magnifies the role of nutrition education as a potential tool in health campaigns to promote healthy eating patterns among college students. Results of this pilot study can inform the design of future nutrition education intervention studies to assess the efficacy of nutrition knowledge on pattern of fat consumption among college students. 
Our results also demonstrate that black race and lower education within a low-income sample were independently related to misidentification of low nutrition and high caloric content foods. Misidentification was generally in the direction of believing that food items were healthier than they actually are. These findings are consistent with USDA survey results that found that black participants were less able than white participants to correctly identify foods with higher fat content . 
If the physician considers that there might be an underlying issue, then thyroid function might be the only reasonable test to perform if there are sufficient grounds on clinical suspicion. Otherwise, consider the drugs and mental status of the person as eating is a common go-to activity for the depressed.