I am not the best speller, but I assure you that Wether is a correct word. Wether is not a misspelling of Weather, or Whether. Wether is the correct term use for a male sheep or goat that has been castrated.
Male lambs, also called ram lambs, are often castrated between 3 and 7 days of age. After that they are referred to as Wethers (sounds like Weather). Male goat kids are called billies, or bucks, and after castration they are called Wethers.
There are several reasons why a sheep producer might castrate his, or her, lambs, although I will point out that my wife and I do not do this to our sheep.
By castrating a male sheep, or goat, the meat does not have as strong of a taste as when the animal is left intact. This is an advantage, or disadvantage, depending on whom a meat buyer is. While many people are accustomed to lamb meat from castrated animals (steers, wethers) some ethnic buyers, such as Muslims, prefer a lamb that is intact.
The act of castrating a lamb can be done several ways, from surgical removal (considered to be the most painful as this is done when the lamb is fully conscious) to the Emasculator which crushes the spermatic cord and blood vessels (no thanks) to the Elastrator, which in my opinion seems like the option I would take if I were going to do this to my own lambs. The Elastrator is also used to remove the tails (docking) and is a tool which places a special elastic band on the testicles, and they fall off a few weeks later.
One caution regardless of the method used to wether an animal, is infection and tetanus, so castrating should only be done on animals once they are vaccinated for tetanus and housed in clean, dry, facilities.