Like Lou said, lightweight and heavyweight shirts refer to the number of "ounces". It's generally how heavy the shirt feels when you wear it (although there is a more technical definition to it

)
A heavyweight shirt general would be 6 oz or above
A midweight shirt would be about 5.5 oz (although this is sometimes referred to as a lightweight shirt on some sites if they are trying to offer a comparison for consumers).
A lightweight shirt to me would be about 5oz or less. Usually "promotional" shirts are printed on lightweight shirts because they are less expensive than heavyweight tees.