There is no special etymology as such. Business could stand for activity or commercial operation. So business end means the end (could be the tip, as in the business end of the fork) which performs or involves the maximum activity or work.
In a long tournament like the World Cup, the knock-out phase could be called business end, because it is the period of intense activity (and also is commercially most popular) involving the best teams.
Googling further, I found this quote from "The Dictionary of Clichés" by James Rogers:
penny for your thoughts — "What's on your mind? (Usually said to someone who is looking pensive.) The saying is from a time when the British penny was worth a significant sum. In 1522, Sir Thomas More wrote (in 'Four Last Things'): 'It often happeth, that the very face sheweth the mind walking a pilgrimage, in such wise that other folk sodainly say to them a peny for your thought.'"
To bless properly means to bestow favor on something, with a strong implication of divine favor and luck. Blessing is a straightforward verbal noun derived from that, and it indicates those things which one has received from others without deserving it, and again has a strong connotation of those things acquired by good luck or providence. So the phrase count your blessings is an invitation to reconsider all of the things that you have which are going well, all of the ways in which you have been blessed, rather than focusing on the negative aspects of your life.
(The phrase "God bless you" following a sneeze is literally an invocation for God to bless the person who has sneezed, i.e. to protect them from disease and demonic influence. However, the phrase has become completely conventionalized, so a person saying it does not necessarily believe in God or demons.)
Best Answer
There is no special etymology as such. Business could stand for activity or commercial operation. So business end means the end (could be the tip, as in the business end of the fork) which performs or involves the maximum activity or work.
In a long tournament like the World Cup, the knock-out phase could be called business end, because it is the period of intense activity (and also is commercially most popular) involving the best teams.