What was the impact of the Portuguese in the Western Hemisphere during the 1500-1600s?

"Depends on what you mean by Western Hemisphere.

If you're following the colloquial "version", then I am assuming you are only referencing the Americas.

However, if you're using the correct term (The half of the earth to the west of the Prime Meridian), then you're referencing North and South America, any Atlantic islands, as well as the western coast of Africa (the part that butts out).

So, I will explain the answer is two parts.

1) (Americas)

The Portuguese had their largest and most notable (to the extent that any other discoveries and excursions remain unacknowledged) influence on Brazil.

The Portuguese in Brazil had an influence on the indigenous people, where they proselytized them, as well as establishing Portuguese as the de facto language.

The 1494 Treaty of Tordesillas "which divided the world outside of Europe in an exclusive duopoly between the Portuguese and the Spanish along a north-south meridian 370 leagues, or 970 miles (1,560 km), west of the Cape Verde islands. However, as it was not possible at the time to correctly measure longitude, the exact boundary was disputed by the two countries until 1777." (Diffie, Bailey (1977). Foundations of the Portuguese Empire, 1415-1580.)

In 1534, the Portuguese encouraged European settlement of Brazil, largely to defend the acquired territories. Later, Brazil became an important asset in Portugal's wars with other European powers.

2) Africa, Indies (Part of Americas), and other islands

Perhaps the most important of Portugal's navigations was that of Bartolomeu Dias's rounding of the Cape of Good Hope (southern tip of Africa). Soon after, the western coast of Africa became a breeding ground for Portuguese forts and trading posts. From these posts, the slave trade became probably one of the major 'industries' for Portugal; it maintained a virtual monopoly on the slave trade for the better part of a century, where about 800 slaves were exported annually, most to Lisbon, the capital. Portugal also had a strong and steady supply of gold from African regions that now form such countries as Mauritania, Morocco, and Guinea, which helped finance its later expeditions into India and Japan.

The Portuguese landfall in small islands in the Atlantic Ocean led to rapid distinctions in European culture and cuisine. The Portuguese were among the first Europeans to use and trade sugar, which they had harvested from the island Madeira. They marketed this sugar in Europe as "sweet salt", which was understandably very rare." ~ UM (Yahoo answers)