Does the treatment of a thyroid disease lead to weight gain, or overweight gain? Or it just stabilize

Depends. On treating under active or overactive thyroid. Under active thyroid causes weight gain and treating it will stabilize or have weight loss. Overactive thyroid can have weight loss and treating will stabilize weight loss and may go back to baseline.
Thyroid disease. Depends on how it is treated. And what is ur thyroid disease.