Have you ever heard of stack (pint) glasses?
Their upper part is bigger so that one can fit into the other perfectly when they are being cleared off the tables in pubs. As a result they can be piled up in a very orderly way one on top of the other almost looking like a column made of glasses. As a result waiters and waitresses can carry more than one very easily.
"in a stack" means one piling up and fitting perfectly on top of the other.
Hope this helps.
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