Can an under-active thyroid (hypothyroidism) cause low body weight or weight loss?

My doctor suggested I go to an endocrinologist because I was complaining about bad sleep, low mood, and a severe lack of energy. I feel tired nearly all the time. The endocrinologist said that these are signs of underactive thyroid. He did a test and said that my thyroid hormone level was just on the low end of the normal range. It might be a problem or it might not. He suggested I try a low dose of thyroid hormone pill for 6 weeks. He didn't feel certain that it was a thyroid problem, so I'm a little wary of trying the medication. Most of my symptoms fit hypothyroidism except for one: I have a very low body weight, even though I eat well. hypothyroidism usually causes weight gain, not loss. Is it at all possible that I can have a low body weight, fatigue, and low mood because of an under active thyroid? The conditions seem to clash a bit.