Little birds can hover, but not soar; big birds can soar, but not hover.
By hovering, I mean (what is called) true hovering: staying aloft by flapping rather than by moving horizontally through the air and doing so for an extended period of time. The kingfisher is probably the largest bird capable of pulling this off.
Occasionally, one does see an osprey or an eagle seemingly hover over a spot below. This is always done when flying into a brisk wind, so the bird actually is moving through the air, but has matched its speed to that of the head wind. Even then, the activity is so energy intensive that the bird can only maintain it for a few moments.
A large bird wants to do this is so it can position itself for an attack on prey.
A Bald Eagle seems to hover in a brisk wind as it eyes a potential prey (probably a duck) below. It did so only briefly before plummeting to the lake surface, but it missed the target.