1843, "to seesaw," alteration of Middle English titter "move unsteadily," probably from a Scandinavian source akin to Old Norse titra "to shake, shiver, totter, tremble," from Proto-Germanic *ti-tra- (source also of German zittern "to tremble"). Meaning "move unsteadily, be on the edge of imbalance" is from 1844.
Noun teeter-totter "see-saw" is attested from 1871 (earlier simply teeter, 1855, and titter-totter in same sense is from 1520s). Totter (n.) "board swing" is recorded from late 14c.; see totter (v.), and compare see-saw.