The story
Probably a frequentative imitative of rhythmic back-and-forth, up-and-down or zigzagging motion, such as teeter-totter, zigzag, flip-flop, ping pong, etc., under the umbrella term of reduplication; also likely influenced by the verbs see and saw of either present or past tense.
Etymology from Wiktionary, CC BY-SA 4.0.