To give someone small beer is to give them a tiny, trifling amount of beer.
Consider the statement "And he handed them each a warm pie and small amount of beer from his own jug, then left them to eat while he rearranged his wares.". Is the statement "And he handed them each a warm pie and small beer from his own jug, then left them to eat while he rearranged his wares." false? Yes/no/unknown