The basis, or that on which an animal walks (Greek, baino, to go, and basis, a footstep). The foot is the foundation- hence, base of a pillar, etc. It is also the lowest part, and hence the notion of worthless. Bass in music (Italian, basso) is the lowest part, or the part for the lowest compass of voice.
Source: Dictionary of Phrase and Fable, E. Cobham Brewer, 1894