You have that backwards thee, thine, thy and thou are formal.
Are you sure about it?
From similarity with the other European languages thou
seems to be more likely to be informal. Also in Shakespeare thou
was used in informal speech.
I know Wikipedia
should be taken with a grain of salt, but ...
Originally the distinction was singular vs. plural. You can see this from some quotes of the KJV, where "thou" is used both for informal and formal contexts, but all singular:
We have "thou" being used from an angel to Joseph:
"And she shall bring forth a son, and thou shalt call his name JESUS: for he shall save his people from their sins."
Then "thou" being used from John the Baptist to Jesus:
"But John forbad him, saying, I have need to be baptized of thee, and comest thou to me?"
From Satan to Jesus:
"And when the tempter came to him, he said, If thou be the Son of God, command that these stones be made bread."
From God to the Isrealites (quoted by Jesus):
"Then saith Jesus unto him, Get thee hence, Satan: for it is written, Thou shalt worship the Lord thy God, and him only shalt thou serve."
Jesus to believers:
"But when thou doest alms, let not thy left hand know what thy right hand doeth"
The blind beggars to Jesus:
"And when Jesus departed thence, two blind men followed him, crying, and saying, Thou Son of David, have mercy on us."
The disciples to Jesus:
"And the disciples came, and said unto him, Why speakest thou unto them in parables?"
Jesus to the unbelievers of Jerusalem:
"O Jerusalem, Jerusalem, thou that killest the prophets, and stonest them which are sent unto thee, how often would I have gathered thy children together, even as a hen gathereth her chickens under her wings, and ye would not!"
The high priests to Jesus:
"Saying, Prophesy unto us, thou Christ, Who is he that smote thee?"
"And saying, Thou that destroyest the temple, and buildest it in three days, save thyself. If thou be the Son of God, come down from the cross."
Jesus to God (quoting the psalms):
"And about the ninth hour Jesus cried with a loud voice, saying, Eli, Eli, lama sabachthani? that is to say, My God, my God, why hast thou forsaken me?"
An alternate usage was "thou" for informal and "you" for formal, although now it seems like the opposite because "thou" is associated with archaic language, which therefore feels formal. This can even be seen in formal writing, places like the RSV where "thou" was retained only to address God, and "you" everywhere else, which certainly makes "thou" seem formal.