Hello! Im a Brazilian Historian and I can help you on this issue. But before I do it, I would like to point two things. The first one, excuse me for the several English language mistakes, im not totally fluent yet. Second, I will show some information about the Brazilian context. I cannot write nothing deep about the effects of this immigration for Portugal and certainly cannot compare this phenomenon with the Spanish case.

That being said, the first thing to clarify is that 700,000 is a exaggereted number. Studies on Colonial Brazil demography are common, and all ressearchers agreed that there is no way to properly calculate. Before 1750s there was nothing like a census and local administration or churches records was irregular or highly inaccurate. The main source to estimate Brazilian population among XVI and XVII centuries are local writings about economy and life, normally wirtten by clergy members.

Those sources normally point the amount of “White”, “Black” and “Indigenous” population, but we have to take the information with some caution for several reasons, one of those being that estimates can show different numbers about the same places. Another important reservation about those writtings are that the “Indigenous” accounted are just we can call “Assimilated Indigenous”, mainly because the vast majority of Portuguese America population was living on the coast. Also, the concept of “White” is not the same as the one used on Europe or USA. A son of Portuguese father and Indigenous mother could easily be considered White. If an individual have some European ancestry, be considered White on Colonial Brazil (even on Contemporary Brazil) is pretty much about social position and lifestyle. Also, the vast majority of the first Portuguese on Brazil was man, so endogamic marriagge was not always an option.

According Maria Luiza Marcílio, among the first Colonial times “The number of Europeans who came to Brazil was relatively low”. The vast majority of those were Portuguese settlers, many times classified as “degredados”, a vague category who included criminals, beggars, tramps gypsies, prostitutes or “Cristãos Novos” (“New Christians”, or forcibly converted Jews). Other Europeans who came to Portuguese America were French, Spanish, Italian, English and Dutch invaders, who settled mainly on provinces like Rio de Janeiro, Pernambuco and Maranhão.

According Padre Anchieta, a priest who immigrate to Brazil on the late XVI century, the Portuguese America’s population in 1585 was 57.600 inhabitants (of course excluding non-assimilated Indigenous), with about 6.000 Whites, 13.000 Africans and 17.500 Christian Indigenous. Historian Contreiras Rodrigues estimates White population on 30.000 in 1600, but lots of historians consider this number overestimated. According Historian Angelo Carrara, Rio de Janeiro Population in 1670 was about 24.000 inhabitants, with just 4.000 of those being “free man” and São Paulo population was about 12.000, with just 1.500 of those being White. According Marcílio estimates, there was 20.000 whites on Portuguese America in 1570, 30.000 in 1580 and 100.000 in 1600.

Portugal was Always concerned about occupy lands on Americas because those lands are also ambitioned by other European nations. But, according Tereza Rodrigues, the country itself was suffering with demographic stagnation among XVII century. Rodrigues points that among 1580-1620 Portugal population faced a decrease of growth, among 1620-1650 the population declined and just on the second half of the century it became to grow again. So, the main way to occupy Brazilian lands was by Africans enslavment.

The first massive wave of Portuguese immigration to Brazil started on the late XVII century, at the same time that Portugal population started to grow again. This trend was linked to gold findings on Minas Gerais region. The opportunity to became instantly rich attracted about 400.000 Portuguese immigrants to Brazil among all over the XVIII century. Just to point how big was this movment, Portugal had about 2 milion inhabitants on 1700. According Marcílio Portuguese immigrants belonged “To every regions, social classes and ocupations. Since peasnants to lower nobles, incluiding craftsman, merchants, priests or just adventurers”. Despite most of those immigratns could not make a fortune with gold itself, lots of economic opportunities was opened on that times, mainly on agriculture and livestock, because lots of cities was founded on the XVIII and had to be supplied with food and other goods. On that times not just the Portuguese came to Brazil, but about 1 million new enslaved Africans and also migrants from several parts of Portuguese America, mainly from the Northeast provinces.

On the beggining of the gold immigration wave, Portugal unsuccessful tried to difficult or forbid new departures to Brazil. But on the second half of that century, Marquês de Pombal (on that times Portugal State Secretary) started to support new waves of Portuguese immigration to low inhabited areas, for guarantee Portuguese supremacy. Those immigrants mainly came from islands like Madeira or Azores. Marcílio points that in 1750 about 6000 Azorians immigrated for Santa Catarina, 4000 Azorian couples immigrated to Rio Grande do Sul and about 500 insular Portuguese arrived on northern provinces of Pará and Maranhão.

After all those trends, a 1798 census showed Brazilian “White” population in about 1 million, or 31% of the total population. Again, is important to consider that a large amount of this million are Brazilian-born whites or even mixed people who are on a relatively good social position. Also, parts of those had another European backgrounds. A new wave of Portuguese immigrants arrived on Brazil just on the beggining of XIX century, after the royal family move to Rio de Janeiro in 1808. In 1818, White population was estimated on 1,3 million.

I also would like to point that Portuguese immigration increased after Independence (1822), mainly between the late XIX and the early XX century. Brazilian government started to execute ambicious immigration programs, to boost the national agriculture, occupy low inhabitated land and “whiten” the population. According Lesser, between 1872-1900 about 380.000 Portuguese immigrated to Brazil. The number of immigrants keeps high, about 514.000 between 1900-1920, about 404.000 between 1920-1940, about 286.00 between 1940-1960. The 1960 decade was the last with a huge amount of Portuguese immigrating to Brazil, about 75.000. Since the 1970s, mainly since the 1990s, the immigration trend looks like inverted, with thousands of Brazilian immigrating to Portugal.

Sources:
ALVES CARRARA, Angelo. A população do Brasil, 1570-1700, uma revisão historiográfica. In: Revista Tempo, volume 20, Niterói, 2014, pp. 1-21.

LESSER, Jeffrey. A invenção da brasilidade. São Paulo: Editora Unesp, 2014.

MARCÍLIO, Maria Luiza. A população do Brasil Colonial. In: BETHELL, Leslie (org). História da América Latina – Volume II: América Latina Colonial. São Paulo: Edusp, 2008, pp. 311-338.

NADALIN, Sérgio Odilon. A população no passado colonial brasileiro: mobilidade versus estabilidade. In: Revista Topoi, volume 4, número 7, Rio de Janeiro, 2003, pp. 222-275.