The size of glasses and cups has been widely variable for pretty much their entire history, but they have always consistently included containers that equal a specific unit of measurement. The wooden masu boxes used for drinking sake originated as standardized measuring cups for portions of rice, for instance. Serving sake in a masu box was a way of showing that you were giving the customer exactly the amount they were paying for. The Romans sold watered-down wine in their taverns by the sextarius, which was roughly equivalent to 1 modern pint, so you'd obviously want a cup that you could completely fill up to ensure you were pouring accurately. Modern pint glasses (though the exact capacity of a pint varies between the US and Britain) are just the same theory of selling a standardized unit of measurement.

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Outside of these unit-specific drinking vessels, their capacity varies widely. Wine glasses through the early 20th century were often quite small and conical compared to the huge bulbous vessels we commonly use today, but those are also glasses that you would repeatedly fill and drain over the course of a night.