Well, this probably starts with diving birds that gave up flying. We have example species for that already, such as penguins. To stay in water for long periods, they're going to need to grow larger so that they can carry a thick layer of insulation, such as blubber: all the example aquatic mammals we have are fairly large for just this reason. Being small and un-insulated in the sea is a great way for a warm-blooded creature to die of cold.
That gets you to creatures that fill similar niches to seals and walruses, who come out of the sea to give birth, and your aquabirds will need to do that to lay and incubate their eggs. The eggs need to be incubated, or the embryos will die of cold if their have a bird's metabolism. Turtles run much cooler.
Having eggs that could float in the sea probably isn't viable, on the grounds of heat loss, and of inability to get enough oxygen through an eggshell. The shell has close to the minimum surface area for its volume, which is exactly what you don't want for a gill system or equivalent.
If you want whale-sized aquabirds, it gets harder. They're too big to come out of the water to lay eggs. I can see two ways to do it:
Give birth to live young, which need to be fairly sizable to carry insulation. But that's boring, and un-avian.
Have major sexual dimorphism. The males grow to the size of whales. The females are smaller, at least for the breeding phase of their lives. They come on land to lay and incubate eggs. They're fed by the males, somewhat like the way real birds feed chicks: the male gathers and pre-digests food, and the female doesn't have to hunt, just go out to sea a little and collect food from him.
It's a bit of a stretch, but it looks sort of right.