Make this one a double

hi there ! As a non-native english speaker I was wondering was does this expression mean ? is that he wants twice as much his glass contain ? even so, it's nearly full, how could she posibly put twice as much in the same glass ??

This is from a webshow called RWBY (pronounced ruby) the character here is being served top shelf whiskey. traditionally, whiskey is poured in 1-1.25 ounce servings, which would fill approximately 1/3rd of the glass. In asking for a double, he is asking for a 2.25 ounce serving of whiskey. the glass is shown full here because the animators made a mistake. do you see the small ice cube closest to the right side of the glass? poured neat (without ice) the middle of that ice cube is approximately where the level of alcohol would be in a single.