The pilot's operating handbook (POH) for a 2005 Cessna Skyhawk 172SP
says the maximum gross weight for takeoff is 2,550 pounds.  I have
heard that when these Cessnas are delivered to other countries, the
trans-oceanic flight requires the removal of seats and the
installation of fuel bladders.  Purportedly, the gross weight for
these flights approaches 5,000 pounds, and the plane still flies. 
Question: What is the actual maximum gross weight at which a Cessna
172SP can be flown and what is your source?

JMH1200 --

Those maximum gross weight numbers are for normal operation.  As you
point out in trans-ocean flights, the weight is exceeded.  Pilots
doing this will get an approval for a takeoff weight, signed off by
the FAA.  See note 14 on Reed Prior's excellent page on flying around
the world in a Mooney.  What is important is to stay well within the
weight-and-balance envelope:

"Note to Pilots" page 
http://www.priortrip.com/

Best regards,

Omnivorous-GA