A little. Thyroid problems play a negligible role in obesity.
The American Thyroid Association states:
In general, 5-10 pounds of body weight may be attributable to the thyroid, depending on the severity of the hypothyroidism.
Most of the weight gain directly associated with thyroid issues is negligible   . In fact, the average weight loss from treatment was 4.3kg, most of which was attributed to the excretion of excess body water  
Pre-existing obesity, a diagnosis of Graves' disease and prior weight loss independently predicted weight gain and weight continued to rise with time.
<a target="_blank" rel="noopener noreferrer" href="https://www.ncbi.nlm.nih.gov/pubmed/11531931" data-toggle="popover" data-trigger="hover" data-content="Highly respected database from the National Institutes of Health" data-title="PubMed Central"></a> </sup>
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- Thyroid.org: Thyroid and Weight
- Weight gain following treatment of hyperthyroidism . Clin Endocrinol (Oxf). (2001) Dale J, et al.
- Relations of thyroid function to body weight: cross-sectional and longitudinal observations in a community-based sample . Arch Intern Med. (2008) Fox CS, et al.
- Weight loss after therapy of hypothyroidism is mainly caused by excretion of excess body water associated with myxoedema . J Clin Endocrinol Metab. (2011) Karmisholt J, Andersen S, Laurberg P.
- Treatment of paediatric hyperthyroidism but not hypothyroidism has a significant effect on weight . Clin Endocrinol (Oxf). (2010) Crocker MK, Kaplowitz P.