I first heard the word "cantilever" when the renovations to old Yankee stadium were described. The old support columns holding up the upper deck were removed because they blocked the view of the field, and the upper deck was thereafter a cantilever. A cantilever is something like a balcony or deck that is supported only on one end, held up by stress on one side, with no support on the other end. We see lots of cantilevered balconies on apartment buildings in New York, but I seldom see them on a regular residential home. Today, I saw a good one.
The support beams of this balcony go far into the house, and really only a small part of the whole beam sticks out. It almost seems like an optical illusion, but we probably see so few because running those beams in is such an intrusive project. On this home, we saw how it was done with the beams sistered to the floor beams through the drop ceiling.
There was another deck directly next door to us, so it was easy to see the contrast between a cantilever deck and a post and beam design, which is far more common.
Why would a cantilever make sense? For the same reason they removed the columns at Yankee Stadium- to avoid obstruction. In this case, there is a patio below the deck, and they wanted to maximize the available space without the encumbrance of beams. And in places like Yonkers, where yards can be small, every square foot of space counts.
Although it looks unbalanced, the thing is quite strong. The ways of calculating stress and the sheer number of beams running underneath that thing distribute the stress evenly. It works. It looks awkward, but it works.