Any cough that lasts for more than 3 months is considered a chronic cough, at any age, and there are many causes of chronic cough.
Combine that with the fact that you snore and that makes two problems that should definitely be investigated by your doctor. Being overweight is often associated with sleep disorders, so you may have to be tested for that.
There is also a condition called acid reflux, where stomach acid bubbles up into the throat. That alone can cause chronic cough and sleep disturbances. It also is more likely to occur in overweight individuals.
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