Huh, well whaddya know, caddy and caddie are different words. I never even knew that caddie wasn't spelled caddy in the singular. I was planning to link to
Cad, but it turns out that'll serve only for golf. People may tee off in golf, but a tea caddy is another kettle of fish entirely. It's from Malay
kati (a weight), which became 'catty', which became caddy. Cool.