Chibi has its roots in kobun, or classical Japanese. The kobun noun tsubi 粒つび, which means “tiny, rounded thing,” eventually evolved into the verb tsubu 禿つぶ, which describes something becoming worn down or sharp edges getting rounded out.
A good example would be a calligraphy brush losing its hairs (because that’s what they used to write back in the days of classical Japanese).
The reading of tsubu eventually changed to chibiru 禿ちびる, and suddenly we’re not too far from chibi.
I had a brief curiosity about what chibi fully means and came across what may be my new favorite post on etymology. Thorough history, examples, usage issue notes and cautions, and even a drawing guide. More word explications should come with an adorable drawing guide.