Even the Mechaber would not require you to satisfy your chiyuv by making you sick. The Torah is דרכיה דרכי נועם and not to afflict yourself because we have to go lechumra. He would agree to just drink more than the usual.
Vashti said to Achashverus that you were a horse keeper for my father and he was able to drink a thousand glasses of wine and did not become drunk but you get drunk after one glass.
I think the connection is that because you are a horse keeper you cannot afford wine so you are not used to drinking, and therefore you get drunk even after one glass, but my father is rich so he drinks a lot and even a thousand glasses will not affect him.
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