"King of Jews" was posted above Jesus by his persecutors, not to honor Him, but to mock Him.
It was common practice amongst the Romans to post the crime of the one crucified on his cross - to identify the reason for the punishment. Jesus Christ was guilty of no crime, although the Sanhedrin brought him before Pilate on false charges of sedition against Caesar.
When Pilate asked Jesus (Mark 15:2) "Are you the King of the Jews?" Jesus answered him "It is as you say." This was the only answer Jesus would give to any of the false charges. Therefore, when Jesus was nailed to the cross (John 19:18-22) Pilate wrote "JESUS THE NAZARENE, THE KING OF THE JEWS." in Hebrew, Latin, and in Greek. The Chief Priests of the Jews read this, and said to Pilate "Do not write 'The King of the Jews'"... But Pilate answered, "What I have written, I have written." Pilate's proclamation was not made to expose the truth, but it did just that. When Jesus comes again, He will be called King of Kings, and Lord of Lords.
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There is another possible answer...

According to some sources Yeshua (most probable Jewish name of Jesus) was a descendant of the line of King David, and as such a threat to not just the Roman imperial establishment in charge in the Roman occupied Kingdom of Judea at the time. This, of course, put him on a collision course with the Roman powers in Jerusalem.

But, to whom Yeshua really was a greater threat was to the Jewish Temple Priests, who were profiteering at the expense of the Jewish pilgrims coming to the Temple in Jerusalem. You must remember that Yeshua (Jesus) had become were irate at the sight of the profiteering going on at the Temple, and he took action, attacking and beating some people profiteering there, as he condemned them for what he was seeing going on at that holy site.

So, in order to get rid of him, the Jewish Temple Priests backed up the accusations of Yeshua trying to be King of the Jews, to make it more likely that the Romans would kill him, and therefore they would eliminate this threat to their status quo.