"Population figures before 1570 are notoriously unreliable, particularly for the native population. From the Conquest until the 1620s, the number of natives fell. Meanwhile, whites, blacks, and persons of mixed ancestry increased in number."--Oxford History of Mexico, p.125

"The conquistadores had followed Cortes for wealth and a better life and therefore expected to benefit from the labor and tribute of the vanquished. Cortes obliged and, acting initially without royal authorization, applied the precedent established in the Caribbean islands of rewarding many of his early supporters with encomiendas. These and subsequent grants of native labor and tribute provided approximately 500 conquistadores and early settlers, about half of whom resided in Mexico City, with the means to support themselves, their families, and retainers without engaging in manual labor." (125)

early 1620s:
native population has dropped from an estimated 10-12 million (though some go as high as 25M) as of 1519 to about 750,000

Another set of estimates:

1519 25.2 M Indians
1532 16.8 M
1548 6.3 M
1568 2.65 M
1580 1.9 M
1595 1.375 M
1605 1.075 M
1625-50 perhaps less than 1 M

from Meyer, Sherman, and Deeds, The Course of Mexican History, p. 199

1650:
total population of Mexico is c. 1.7 million:

group
number
peninsulares
14,000
criollos
171,000
mestizos (white/indigenous)
109,000
indigenous people
1.3 million
mulattoes (black/indigenous)
116,000
blacks
35,000

1793:
Despite crop failures and epidemics, the population expanded between the mid-17th and mid-18th centuries. Total population is estimated at 3.8 million :

group
number
whites
685,000
castas (mixed-race people: indigenous/white; indigenous/black; black/white)
788,000
indigenous people
2.3 million
blacks
6,000

from Foster, A Brief History of Mexico:
"Criollos could not hold royal office, because the Crown suspected that their place of birth tarnished their loyalty. Only whites were permitted to wear European silk finery, ride horses, and be called damas and caballeros. So important was it to pretend to be pure white, and so unlikely was that to be the case in New Spain, that the Crown would certify all Indian or African blood 'extinguished' in a family--for a fee." (93)

"Although considered wards of the Crown and church, Indians suffered abominably whether because of debt peonage or mine labor. At least one-half of Indian children died in their first year; 75% died in early infancy. Excluded from formal education, their lot became that of illiterate and abjectly poor laborers and peasants." (94)