I know that's not a lot of alcohol
Any amount of alcohol is a lot of alcohol for an alcoholic. When my EXAG relapsed about 5 years ago, it was with 2 glasses of wine at a work dinner- Not a lot of alcohol. Fast forward many years and the drinking is straight Vodka and a potential upcoming jail sentence. It will get worse.
From your posts, it appears that your GF likes to plan her drinking, and get you involved with it. This is her manipulating way of getting you to "approve" of her drinking. If you buy the beer, you are telling her it is Ok.