pia.

Principal English Translation: 

to hold, guard, have, keep; to observe (when it appears in front of a reference to a festival or an order for something to be observed);to maintain chastity and celibacy (mopia)

Orthographic Variants: 
pie, piye, piya
IPAspelling: 
piɑ
Alonso de Molina: 

pia. nino. (pret. oninopix.) guardarse de algo.
Alonso de Molina, Vocabulario en lengua castellana y mexicana y mexicana y castellana, 1571, part 2, Nahuatl to Spanish, f. 81v. col. 1. Thanks to Joe Campbell for providing the transcription.

pia. nite. (pret. onitepix.) guardar a otro.
Alonso de Molina, Vocabulario en lengua castellana y mexicana y mexicana y castellana, 1571, part 2, Nahuatl to Spanish, f. 81v. col. 1. Thanks to Joe Campbell for providing the transcription.

pia. nitla. (pret. onitlapix.) guardar alguna cosa.
Alonso de Molina, Vocabulario en lengua castellana y mexicana y mexicana y castellana, 1571, part 2, Nahuatl to Spanish, f. 81v. col. 1. Thanks to Joe Campbell for providing the transcription.

Horacio Carochi / English: 

pia = to hold, guard, have
Horacio Carochi, S.J., Grammar of the Mexican language with an explanation of its adverbs (1645), translated and edited with commentary by James Lockhart, UCLA Latin American Studies Volume 89 (Stanford: Stanford University Press, UCLA Latin American Center Publications, 2001), 509.

Lockhart’s Nahuatl as Written: 

(1), nic. to guard, keep, hold, have. in addition to older meanings gradually becomes equivalent to Sp. tener, to have. Class 2: ōnicpix, often ōnicpīx; the i of pia was probably originally long.
(2), nitlah. to be on guard, in charge (with a locative expression). origin of h unknown. 229
James Lockhart, Nahuatl as Written: Lessons in Older Written Nahuatl, with Copious Examples and Texts (Stanford: Stanford University Press and UCLA Latin American Studies, 2001), 229.

Attestations from sources in English: 

ayac tlen quimopieliaya = No one had anything (Santa María de los Angeles Huitzillan, Toluca Valley, 1741)
Caterina Pizzigoni, ed., Testaments of Toluca (Stanford: Stanford University Press and UCLA Latin American Center Publications, 2007), 89.

nican Ospital oquimoyecoltilique yn cocoxcatzitzintin yhuā oquimopielique yn imanima = they served the unfortunate sick here in the hospital and they guarded their souls
Fray Alonso de Molina, Nahua Confraternities in Early Colonial Mexico: The 1552 Nahuatl Ordinances of fray Alonso de Molina, OFM, ed. and trans., Barry D. Sell (Berkeley: Academy of American Franciscan History, 2002), 132–133.

By 1600, pia most often meant to have. It could act much like tener, to have, plus a number of years, in the formula for expressing age:
quipia 15 xihuitl amo quipatia in tlacalaquilli = She is 15 years old; she does not pay tribute [yet]. (This was a common formula in marriage records.)
Rebecca Horn and James Lockhart, "Mundane Documents in Nahuatl," in James Lockhart, Lisa Sousa, and Stephanie Wood, eds., Sources and Methods for the Study of Postconquest Mesoamerican Ethnohistory, Preliminary Version (e-book) (Eugene, Ore.: Wired Humanities Project, 2007, 2010), 10.

quipiezque = they are to observe it
(Mexico, late seventeenth-century) (Techialoyan manuscript from San Cristóbal Texcalucan and Magdalena Chichicaspa)
James Lockhart, personal communication, May 23, 2008.

oquixoxocoque noye quipiaz yn nonamic = They invaded it, (but) my wife is to have it also. (Tlaxcala, 1566)
Beyond the Codices, eds. Arthur J.O. Anderson, Frances Berdan, and James Lockhart (Los Angeles: UCLA Latin American Center, 1976), Doc. 1, 46–47.

çaniuh quipixtiyez = He is to keep it as it is. (Tlaxcala, 1566)
Beyond the Codices, eds. Arthur J.O. Anderson, Frances Berdan, and James Lockhart (Los Angeles: UCLA Latin American Center, 1976), Doc. 1, 52–53.

mopiaz = it will be kept; or, the fiesta will be observed
mopiez = will be observed as in that which we have issued or ordered
motlapielia = is in charge, stands guard
Personal communications from James Lockhart. This term appears in the Techialoyan manuscript from Ocoyacac. Mopiez also appears in Techialoyan texts

ticpixtoque = we hold
Byron McAfee, translation of the Techialoyan manuscript from Santa Mara Zolotepec or Ocelotepec; University of California, Los Angeles, Special Collections

The term mopia (also mopiya) meant "to keep or guard oneself," and terms derived from it were used to express the notions of celibacy and chastity. (late seventeenth century, Central Mexico)
Louise M. Burkhart, Before Guadalupe: The Virgin Mary in Early Colonial Nahuatl Literature, Institute for Mesoamerican Studies Monograph 13 (Albany: University at Albany, 2001), 30.

huel mopieya = quite chaste (early seventeenth century, Central Mexico)
Louise M. Burkhart, Before Guadalupe: The Virgin Mary in Early Colonial Nahuatl Literature, Institute for Mesoamerican Studies Monograph 13 (Albany: University at Albany, 2001), 144.

"Nahuatl does not have a word for 'to have' .... It is true that piya 'to guard' can sometimes be translated with 'to have', but this involves the sense of 'to have in a chance manner', 'to have on one', for example." For example, "Cuix ticpiya ichtli? = Do you (singular) have a thread (on you)?" Or, Nicān nicpiya ōntetl tomātl = I have two tomatoes here.
Michel Launey, An Introduction to Classical Nahuatl, translated and adapted by Christopher MacKay (Cambridge: Cambridge University Press, 2011), 100.

Attestations from sources in Spanish: 

quimopilis ynopiltzin Juan nicnomaquilia = la ha de tener mi hijo Juan [y la tenga], que se la doy (Santa Bárbara Maxoxotlan, 1592)
Vidas y bienes olvidados: Testamentos indígenas novohispanos, vol. 1, Testamentos en castellano del siglo XVI y en náhuatl y castellano de Ocotelulco de los siglos XVI y XVII, eds. Teresa Rojas Rabiela, Elsa Leticia Rea López, y Constantino Medina Lima (Mexico: CIESAS, 1999), 222–223.

ma Dios mitzmopieli inipan ixquich ahmo qualli = Dios te guarde de todo mal.
Pedro de Arenas, Vocabulario Manual de las Lenguas Castellana, y Mexicana (Mexico: Henrico Martínez, 1611), 2.

zemicac mopiez = que sea guardado para siempre
En referencia al documento del pueblo. Fuente: Anneliese Monnich, "El Altepeamatl de Ocoyacac, México," Indiana 2 (1974), 168.

Ticpi:a yec tiu:tac, Ton:o. Pa:mpadiush Juanita, kenhalla. = Que tengas buenas tardes, Ton:o. Graci:as Juanita, igual. (Sonsonate, El Salvador, Nahuat or Pipil, s. XX)
Tirso Canales, Nahuat (San Salvador: Universidad de El Salvador, Editorial Universitaria, 1996), 21–22.

auh in arçob[is]po no yaopialoya yvan in tlatoque oydoresme moch pialoya = Y el arzobispo tambíen era vigilado militarmente, junto con los señores [tlatoque] oidores, todos eran vigilados. (ca. 1582, México)
Luis Reyes García, ¿Como te confundes? ¿Acaso no somos conquistados? Anales de Juan Bautista (Mexico: Centro de Investigaciones y Estudios Superiores en Antropología Social, Biblioteca Lorenzo Boturini Insigne y Nacional Basílica de Guadalupe, 2001), 148.