{{11}}pat (adv.) "apt, suitably," 1570s, perhaps a special use of PAT (Cf. pat) (n.) in sense of "a hitting" the mark. The adjective is 1630s, from the adverb.
{{12}}pat (n.) c.1400, "a blow, stroke," perhaps originally imitative of the sound of patting. Meaning "light tap with hand" is from c.1804. Sense of "that which is formed by patting" (as in pat of butter) is 1754, probably from the verb.
{{12}}pat (v.) "to tap or strike lightly," c.1600; see PAT (Cf. pat) (n.). The nursery rhyme phrase pat-a-cake is known from 1874. Related: Patted; patting.

Etymology dictionary. 2014.