In the USA, there is a company called "Hefty" that makes bags for garbage. They have very famous TV advertising that uses the word "wimpy" to describe all the bags made by other companies -- bags that break when you put a lot of garbage in them are the ones called "wimpy"! The name of the company is a real word: "hefty" is a word you can look up and is a standard word that can be used in any situation. Wimpy is its opposite, but is slang and would not be used in formal writing or formal speaking.

To whom would you say that? ~To people who you believe are acting weak when you think or you know they could be stronger (either emotionally or physically). Or it can also be a way of saying "Be a man." Situation(Physically): Your friend is carrying a bag filled with books. He is complaining that is too heavy. You would reply "Don't be wimpy" or "Don't be a wimp", because you are carrying twice as much as he is. So you would see no reason for him to complain. Situation(Emotionally): It all depends on your point of view.