There is actually no real records available or even an inventor who created the actual seesaw. The earliest records that mention a seesaw was back in 1640. The reference was to a song that talked about two men cutting a log with a two-man saw. This was a back and forth motion from the saw and the was derived from the French word "sie" because of the back and forth movement of the saw.
The second mention of this was in 1704 when people were playing a game on a plank. This was a balance gamed called Anglicisation. Again this came from the French word "ci-ca" This again was because of two people sitting on a plank and trying to balance.
Across the world, the seesaw goes by many different names. In America, this can be called a teeter-tooter or even a teeterboard. I would guess back in 1704 when a person heard the French name for the game "ci-ca" they had no idea how to spell this and if hear this you could easily think it was spelled seesaw. That is my guess on this one.