I've also had a similar experience. I'm 5'6, and I started at 129, and now I'm somewhere above 140 (I refuse to weigh myself until I feel better). The weight gain happened suddenly, in the month of January, one month in to the diet change. I've been very proactive about my health, so this was a surprise. Like, you, I'm still a healthy weight, but I don't fit into my clothes, and I'm pudgy where I never was before. I was lucky to see a doctor who sent me to have my thyroid antibodies tested. Sure enough, I'm positive, and I have FreeT3's that are low, out of the normal range. This points to Hashimoto's. I am seeking an endocrinologist who will help me now and hope to feel better soon.
Do you have any other hypothyroid symptoms?
Good luck, and be sure to include thyroid autoantibodies tested along with FT3s and FT4s.