Would and might are two words of the English language. They are both modal verbs. One of the key differences between them is that each verb is the past tense of other words. Would is the past tense of will. Might is the past tense of will. They both share that they are formed from Old English words, but they differ in the type of Old English word they come from.
It would come from wolde while might comes from meat. Would is used to describe the possibility of doing something. For example, "I would go home early if I were you." Might is also used for possibility or to request something such as "I might go home early."