The headword, a two-ending adjective, compounds para/ with the verb a)ei/rw: I raise up beside (cf. Chantraine s.v.; Leumann, p. 222). It appears at three widely separated passages, all supported by scholia, in Homer's Iliad: 7.156 (web address 1), 16.471 and (in the accusative at) 16.474 (web address 2), 23.603 (web address 3). But each instance evidently requires a different figurative variant of the headword's literal meaning (Kirk, pp. 255-6):
(i) At 7.156, Nestor (OCD(4) s.v. Nestor(1)) recounts his youthful slaying of Ereuthalion. Nestor looked down at the Arcadian hero sprawled upon the ground, his huge frame outstretched as if having been hung. The etymology of parh/oros encourages this vivid imagery. But against this Leumann (op. cit., pp. 225-231) suggested that the received text for this verse in fact originates from an Iliadic poet's mistaken interpretation of the second passage.
(ii) At 16.471, the parh/oros is a trace-horse, an extra horse harnessed alongside the chariot's yoked pair; cf. pi 628. A scholion to this verse describes the trace-horse as o( parh|wrhme/nos i(/ppos, the horse having been hung beside; cf. pi 561. Leumann (ibid.) proposed that, when Pedasos lay in the dust after having been killed by Sarpedon (OCD(4) s.v.), the poet interpreted parh/oros at 16.471 as sprawling, not trace-horse, and then imported the erroneous interpretation into Nestor's Book 7 storytelling. Recent commentators on the Iliad have concurred (e.g. Janko, p. 379).
(iii) The Suda's gloss for this entry reflects the third figurative usage of the headword; see further n.1 below.
[1] The glossing participle is perfect middle/passive, masculine nominative singular, of the verb pari/hmi; cf. pi 347, pi 649, and see LSJ s.v. Now Menelaus (OCD(3) s.v. Menelaus(1)) uses parh/oros for past irrationality on the part of Antilochus (OCD(4) s.v.) at Homer, Iliad 23.603 (with scholia). This might be metaphorical of typical trace-horse behavior (Kirk, p. 255) or, as the gloss appears to suggest, both a body and a mind can be dropped alongside. For this meaning, cf. Archilochus fr. 130.5 West; Apollonius Sophistes, Homeric Lexicon 128.12-13 Bekker; Etymologicum Magnum 653.41-54; and Hesychius s.v.