I am trying to determine which sea ports in South America are the
busiest. It doesn't matter whether the criteria is dollar value of
goods, weight, number of containers or whatever. Just as long as it is
not someone's opinion or guess.

Hello there

According to US Customs Today, Sept 2002, Guayaquil is South America's
busiest Pacific seaport.
http://www.customs.ustreas.gov/xp/CustomsToday/2002/September/international.xml
- From US Customs Service

"Manzanillo International Terminal (MIT) has been recognized not only
as Latin America's busiest container port, but also one of the world's
most productive, handling more than 1 million TEUs a year."  - This
port is Panamanian and is included in South American lists though the
country itself is Central American - So I will leave it up to you to
decide.
http://www.tideworks.com/eng/products/casestudies/MIT.html - From
Tideworks Technology

The Journal Of Commerce Special lists Santos, Brazil as South
America's busiest port. - second paragraph down
http://www.labournet.org/docks/9812/santos.htm - From Labournet.org

Another reference to Santos, Brazil as South America's busiest port: -
"LATIN AMERICA & EUROPE: Santos showdown may break dock unions' grip:
Latin America's busiest sea port has been paralysed by strikers
fighting to keep control of hiring workers, writes Raymond Colitt"
Financial Times; Apr 6, 2001 

However as this quote from the American Association of Port
Authorities states: - "The question is ambiguous, however, since ports
can be compared in many different ways - by volume or value of trade,
number of cruise passengers, revenues, and storage capacity, as
examples."

So, since you mentioned "containers," that might be the best way to
go.  The measurment is by TEUs per year. - "TEU = “Twenty-Foot
Equivalent Unit,” a standard linear measurement used in quantifying
container traffic flows.  As examples, one twenty-foot long container
equals one TEU while one forty-foot container equals two TEUs (i.e.,
40'÷ 20' = 2)." - from AAPA

This from the American Association of Port Authorities - Port Industry
Statistics  -  http://www.aapa-ports.org/industryinfo/statistics.htm
For container handling, the top five are, measured in TEUs per year,
figures for year 2000:

Port of Buenos Aires, Argentina - 1,126,712

Port of Santos, Brazil - 800,898

Port of Rio Grande, Brazil - 317,718

Port of Valparaiso, Chile - 256,386

Port of Rio de Janeiro - 217,332

Those figures were culled from this list:
http://www.aapa-ports.org/pdf/Container_CSAmerica.PDF - you will find
figures for other ports as well.  - a PDF file
This will take you to the reports and definitions page of the website:
http://www.aapa-ports.org/industryinfo/statistics.htm

Search - Google
terms - south american ports, south america's largest ports, south
american ports by tonnage, south american ports by teus

If I may clarify anything, please ask.

Cheers
digsalot

Bravo!