The Polynesians have two different terms for 'spinning', hiri and hiro: 
Hiri

1. To braid, plait, tress (hair, threads). 2. To rise in coils (of smoke). 3. To hover (of birds). Vanaga.

1. To elevate, to mount. Hiriga, to elevate; elevation, mounted, ascension, assumption, declivity; hiriga mouga, hillside. Hirihiri, a swing, seesaw. P. Pau.: iri, to be put up in a place, to lodge. Mgv.: iri, placed in a higher position than the observer, as a box on a high shelf. Ta.: iri, to lodge or stick up in a place. The germ signification is 'above, higher'. In Samoa it is used most commonly in a tropical sense, but the primal sense is sufficiently retained in the signification to lodge, to stick in, to show general concord with Rapanui and particular harmony with the other languages of Southeast Polynesia. 2. To make a bag; taura hiri, to make a cord; rauoho hiri, plaited hair; hirihiri, frizzed; rauoho hirihiri, lock of hair. P Mgv.: hiri, wo weave, to plait; akahiri, to make a mat. Mq.: hii, large plait of coconut fiber. Ta.: firi, to plait, to braid. When we interpret in the sense of local conditions Père Roussel's definition 'to make a bag' the concord is perfect, for bags are woven. The germ sense is plainly the act of twining in and out, over and under, which, with specific differences due to manner and material, may result in plaiting or weaving; see hiro. 3. To go, to walk, to voyage, to arrive, to appear; hiri tê reka, to go without noise; hiri koroiti, to go softly; hiri tahaga no mai, to go without a halt. Hiriga, voyage, journey; hiriga hakapa, to go by twos; hiriga hipa, to go obliquely; hiriga kokekoke, to go by sudden steps; hiriga okorua, to go by twos; hiriga tahataha to go across; hiriga tekiteki, to go on hopping; hiriga tê mataku, to go on fearlessly; hiriga totoro, to go on all fours; hiriga varikapau; to go in a ring; hiriga veveveve, to go boldly. Churchill.

Pau.: Hirinaki. 1. To incline, to slope. Ta.: hirinai, to rest upon. Ma.: irinaki, to rest upon. 2. To be apprehensive. Ta.: hirinai, to apprehend. Churchill.

Mgv.: Aka-hiria, to enquire after. Sa.: sili, to ask, to demand. Hirihiri, to fish for turtle. Mq.: fiifiii, a small net for taking turtle. Churchill.

Hiro

1. A deity invoked when praying for rain (meaning uncertain). 2. To twine tree fibres (hauhau, mahute) into strings or ropes. Vanaga.

To spin, to twist. P Mgv.: hiro, iro, to make a cord or line in the native manner by twisting on the thigh. Mq.: fió, hió, to spin, to twist, to twine. Ta.: hiro, to twist. This differs essentially from the in-and-out movement involved in hiri 2, for here the movement is that of rolling on the axis of length, the result is that of spinning. Starting with the coir fiber, the first operation is to roll (hiro) by the palm of the hand upon the thigh, which lies coveniently exposed in the crosslegged sedentary posture, two or three threads into a cord; next to plait (hiri) three or other odd number of such cords into sennit. Hirohiro, to mix, to blend, to dissolve, to infuse, to inject, to season, to streak with several colors; hirohiro ei paatai, to salt. Hirohiroa, to mingle; hirohiroa ei vai, diluted with water. Churchill.

Ta.: Hiro, to exaggerate. Ha.: hilohilo, to lengthen a speech by mentioning little circumstances, to make nice oratorial language. Churchill.

When the moon is rising from the water at the western horizon the night is Ohiro (the first night of the moon according to Englert). The name presumably alludes to her rising being the result of a kind of waterspout, spinning around itself (pú ohirohiro).

Fornander has traced the word back to the old Indo-European languages, and his synopsis is good to remember when trying to read rongorongo texts: 

"HILI, v. Haw., to braid, plait, twist, turn over, spin; wili, id.; wili, s. a ribbon a roll; wili-wili, to stir round, to mix; another dialectical variation is hilo, to twist, turn, spin.

Sam., fili, to plait, as sinnet; filo, to mix, s. twine, thread; vili, a gimlet a whirlpool.

Marqu., fau-fii, twist, braid.

N. Zeal., wiri, id.

Rarot., iro, id.

Tah., firi, id.; hiro, id.

Fiji., siri, askew, not nicely in a row, wrong, in error.

Tagal and Bisays, hilig, a woof.

Greek, είλω, to roll up, to press together, pass to and fro, to wind, turn round; έλισσω, turn round or about, roll, whirl; έλιξ, adj., twisted, curled; s. anything of a spiral shape, twist, curl, coil; ίλλω, to roll, of the eyes, to squint, look askance; ίλλος, squinting; ίλλας, a rope, band; ίλιγξ, a whirlpool.

Sanskr., vel, vehl, to shake, tremble; vellita, crooked; anu-vellita, a bandage. To this Sanskrit vel Benfey refers the Greek είλω, the Latin volvo, and the Gothic walojan. Liddell and Scott also incline to connect είλω and volvo with the same root.

To me it would seem as if the Sanskrit vrij, whose 'original signification', Benfey says, is 'to bend', and the Sanskrit vrit, whose 'original signification', Benfey says, is 'to turn', were nearer akin to the primary form from which the Greek είλω, ίλλω, and the Polynesian hili, wiri, descend: that primary form being vri, now lost to the Sanskrit, with a primary sense of to bend, twist, turn over, braid, and of which vel, vell, or vehl, is possibly another secondary and attenuated form. With such a Sanskrit vŗi. surviving in vŗij and vŗit, the derivation of the Latin filum, thread, as twisted, spun; of the Latin varus, bent asunder, parting from each other, varix, crookedness; of the Saxon wile, deceit; of the Swedish willa, confusion, error, wilse, astray, becomes easy and intelligible." (Fornander)