An underactive thyroid (hypothyroidism) genuinely slows metabolism — but the effect is often overstated, and the most important fact is this: once hypothyroidism is properly treated and you are euthyroid (normal TSH), your metabolic rate returns to normal. Weight gain from untreated hypothyroidism is usually modest (commonly a few pounds of fluid and slowed clearance, not large fat gain).
The American Thyroid Association (ATA) notes that while hypothyroidism can cause weight gain, it is typically 5–10 pounds and resolves largely with treatment. This hub explains the metabolic mechanism and links a calculator that applies a conservative adjustment only for the untreated/suboptimally-treated state.