It is important to understand that weight is entirely a function of input and output. The input is the food you eat and the calories contained therein. The output is your energy output. To lose weight the output needs to be greater than the input. It is that simple. Do not believe any of the diet fads. If you are currently not gaining or losing weight then just burning 300 extra calories per week or eating/drinking 300 calories less per week (2 sodas for example or a small burger) WILL make you lose weight - in this case around 5 pounds of fat per year.
Your doctor can easily arrange for you to take a blood test to measure the concentration of thyroid stimulating hormone (TSH). If the test comes back and everything looks good, your thyroid gland is probably fine. For a more exact diagnosis, you can ask them to measure the actual levels of thyroid hormones in the blood (T3 and T4), as sometimes these are low even if the TSH is within the fairly broad normal range.
The Mayo Clinic Diet is generally safe for most adults. It does encourage unlimited amounts of vegetables and fruits. For most people, eating lots of fruits and vegetables is a good thing — these foods provide your body with important nutrients and fiber. However, if you aren't used to having fiber in your diet, you may experience minor, temporary changes in digestion, such as intestinal gas, as your body adjusts to this new way of eating.