La avería, o derecho de avería, era un impuesto ad valorem sobre el comercio colonial de los siglos XVI y XVII en España; se imponía sobre los mercaderes o las mercancías. Asimismo, incluía a los pasajeros que pasaban a Indias.

Formally, one of the meanings of "avería" in the Oxford Dictionaory is "damage"

So, given the context, possibly what it means is:

damage to the indigenous people

Results 1 - 10 of about 14 for "damage to the indigenous people". (0.46 seconds)
Search Results

1.
Land Rights of the Indigenous Peoples of the Chittagong Hill ... - Google Books Result
by Rajkumari Chandra Kalindi Roy - 2000 - 231 pages
An alternative site was proposed further upriver which would have caused less damage to the indigenous people, but this was rejected as being too near the ...
books.google.com/books?isbn=8790730291...
2.
Brazil - Brazzil Mag - Indians Get Land in Brazil and Governor ...
... but they regret that many of them have polluted rivers and cleared forest areas, causing incalculable damage to the indigenous people. ...
www.brazzilmag.com/content/view/2164/ - 95k - Cached - Similar pages -
3.
Defending Sudan's Black Muslims
... the real danger is that the killing will be ignored until the genocide and ethnic cleansing do irreparable damage to the indigenous people of Darfur. ...
www.defenddemocracy.org/index.php?option=com_content&task=v... - 35k - Cached - Similar pages -
4.
Using Community Informatics to Transform Regions - Google Books Result
by Stewart Marshall, Wallace Taylor, Xing Huo Yu ... - 2004 - Business & Economics - 302 pages
The notion that 'the pen is mightier than the sword' was reinforced by Kamira when she asserted that the greatest damage to the indigenous people of New ...
books.google.com/books?isbn=1591402786...
5.
Atkinson - May 06
... on ‘liberal fantasy’, meaning the notion that the British acquisition of Australia could have been achieved without damage to the indigenous people. ...
home.vicnet.net.au/~abr/May06/Atkinson%20review.htm - 54k - Cached - Similar pages -
6.
EDITORIAL
This situation, along with past successive colonizations of Taiwan, has brought enormous damage to the Indigenous people of the island territory. ...
www.ibiblio.org/ahkitj/wscfap/arms1974/PRAXIS/1995/1995 Q3/... - 8k - Cached - Similar pages -
7.
The Devil and James McAuley - Google Books Result
by Cassandra Pybus - 1999 - History - 321 pages
... work with Hogbin on a committee to establish compensation for war damage to the indigenous people, and Black to a Directorate mission in Borneo in 1945. ...
books.google.com/books?isbn=0702231118...
8.
United Nations Office at Geneva | News & Media | COUNCIL DISCUSSES ...
... and the consequent health damage to the indigenous people, and hoped that he would be able to add a visit there to his already crowded schedule for the ...
www.unog.ch/80256EDD006B9C2E/(httpNewsByYear_en)/A4461FC9E2... - 85k - Cached - Similar pages -
9.
the syracusan
Second, we can give this gift without fear of psychological damage to the indigenous people or resentment at our donations—when personal health is at stake, ...
syracusan.blogspot.com/ - 194k - Cached - Similar pages -
10.
Indians, Oil, and Politics: A Recent History of Ecuador - Google Books Result
by Allen Gerlach - 2003 - History - 286 pages
The lawsuit failed; there was no compensation for environmental or social damage to the indigenous people or to other Ecuadoreans. ...
books.google.com/books?isbn=0842051082...

Mike :)

Avería = average in the maritime field... So, Please see this enlightening reference

http://www.articlearchives.com/law-legal-system/admiralty-la...