The word stale derives from sta-, the root of an old Germanic verb meaning to stand still. Originally, it referred to the process of letting beer stand, or age, in the barrel before being drunk. In those days, beer got better if you allowed time for the dregs to settle to the bottom and for the fermentation to finish. By Shakespeare’s time, stale was being used as an adjective in its modern sense: a decrease in quality due to a loss of freshness or a decrease in value due to overuse. Here stale is used in this second sense. Cassius is saying that if he made oaths of love to everybody claiming to be a friend, then those oaths wouldn’t be worth much. But Shakespeare’s audience would hear a second, more humorous meaning in this phrase.