Great question — answering as the UphillTech team:
It's to do with US drinking/alcohol laws. Apparently it's illegal to carry open containers of alcohol, so by placing it inside a brown paper bag, this claims "it's not open" and "I'm not really drinking it". The brown bag would be the one the store placed it in at purchase. I don't know whether this is an actual law across all 50 States or whether it has just become 'movie shorthand' to explain why an outdoor drinker might 'have a problem with alcohol' sufficient that they can't wait til they get home, or that they don't have a home to take it to.
Full answer by Tetsujin: https://movies.stackexchange.com/a/114064 (CC BY-SA 4.0).
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