The story
Probably connected to tidy. Granville (1950) claims that it is "from tidy, influenced by titivate", while Jolly (2018) states that it "appears merely to be a whimsical corruption of tidily".
Etymology from Wiktionary, CC BY-SA 4.0.
tiddly suit
Today it means: A sailor's best uniform, often tailored and not strictly to regulation. Full definition →