According to the Alaskan Fish And Game department,
"The wings of an eagle need to support the eight to 12-pound bird as
well as whatever the bird is carrying, and best estimates put the
lifting power of an eagle at four or five pounds. ..."
But as the article continues,
"Lift is dependent not only on wing size, but on airspeed. The faster
a bird (or plane) is flying, the greater the lift potential. An eagle
that lands on the beach to grab a fish, and then takes off again, is
limited to a smaller load than an eagle that swoops down at 20 or 30
miles an hour and snatches up a fish. That momentum and speed gives
the bird the ability to carry more weight."
This may or may not explain Amazing Bird Records for:
greatest weight-carrying capacity: bald eagle lifting a 6.8 kg (15 lb)