Using font sizes of 13px or more is necessary for readability. In fact, some of us are even moving to sizes like 16px.
Here's an exercise for you. Find a book. Any book, but make sure it's nicely printed. Now, hold it as you would read it, in front of your monitor. To make the text on your interface readable, you must increase its size so it has a similar magnitude to the glyphs on the book. Because the monitor is further away from the book, you're going to need to go reasonably high.
For this exercise, you'll find that 11px isn't be nearly enough - and true enough, find real users, and you'll discover that the 'standard' 11px is unbearably small, especially for older users (middle age plus) whose eyesight has degraded.
As for field sizes, I wouldn't say SE's elements are all that large. But Fitt's Law does mandate a minimum target size in order for users to quickly click items, and naturally, if font sizes are increased, the field boxes that contain text have to get bigger too.
Finally, on the matter of disappearing labels - users will already know the content they want to enter by the time they start typing. Especially with slot-in answers on personal data. Of course, such a design means a user can't seek a particular field by label. But that's a tradeoff worth making, as self-labelling fields require that users only use a single eye fixation to spot both label and input.