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"expel saliva," Old English spittan (Anglian), spætan (West Saxon), from PIE *sp(y)eu-, of imitative origin (see spew). Not the usual Old English word for this; spætlan (see spittle) and spiwan (see spew) are more common. Meaning "to eject saliva (at someone or something) as a gesture of contempt" is in Old English.
"saliva," c.1300, from spit (v.). Meaning "the very likeness" is attested from c.1600 (e.g. spitting image, attested from 1901); cf. French craché in same sense. Military phrase spit and polish first recorded 1895.
"sharp-pointed rod on which meat is roasted," Old English spitu, from Proto-Germanic *spituz (cf. Middle Dutch spit, Swedish spett, Old High German spiz, German Spieß "spit," German spitz "pointed"), from PIE *spei- "sharp point" (see spike (n.1)). This is also the source of the word meaning "sandy point" (1670s). Old French espois, Spanish espeto "spit" are Germanic loan-words. The verb meaning "to put on a spit" is recorded from c.1200.