| Eagles, hawks and owls are very limited in the weight they can carry. They certainly cannot "lift 4 times their own weight" as a recent post claims.
The Alaska Fish and Game Department, in a good spot to observe eagles, points out that "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.
Biologist Ron Clarke earned his masters degree studying birds of prey, and he’s a falconer who trains raptors .... "On a wide-open beach, I have no doubt that an eagle with a full head of steam could pick up a six- or eight-pound dog and just keep on going," Clarke said. "If it landed to kill a ten-pounder, and then tried to pick up and fly from a dead stop, could it get off the ground? Probably not."
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http://carnivoraforum.com/index.cgi?board=zoological&action=print&thread=4547 discusses this issue, and has a video of a Golden Eagle taking a small goat (they don't specify the size of the goat).
The best the eagle can do, even with the elevated take-off from the cliff - is a very steep angled glide. You see it trying to flap and then shift to fully fanned out wings for maximum braking. Unfortunately they don't show the landing.
Hawks will gorge on a kill that is too large to carry, digest it (they have very fast digestive systems), defecate to lighten their load, then go back and carry the remains off if they are small enough now to lift.
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So if your 12-pound pooch goes missing, it was coyotes. | 
