Alright, I do understand the Wide Nine. I call it that cheap shit cheeser like to do in Madden. I just don't get why the Eagles use it.
Essentially, the reason why it's called the wide nine is because of the gaps.
This a two-TE I-Form set. The gaps are indicated in red. Between the C-G is 1, G-T is 3, T-TE is 5, and outside the TE is 7. This is just to indicate distance. Now, you know that asshole in Madden who likes to move their DE as far to the outside as they can so he can have a straight shot at the quarterback without being completely out of position? That's essentially the "nine gap".
So, those are the gaps. Here's a base 4-3 defense with a diagram of the gaps.
You can see where the defenders are supposed to go and the gaps they're responsible for. The DEs have to go against the TE/T and use creative moves to get around their man. Here's the Wide Nine.
The Wide Nine sucks all creativity out of the equation and says "just run in a straight line to the quarterback." See how the ends are lined up farther than the linebackers? This now leaves your tackles and your linebackers as your only five in the box. You're asking your defensive tackles to absolutely take up space and your linebackers to be at their absolute best.
Now, obviously, the I-Form isn't really where you want to use the Wide Nine. The Wide Nine succeeds as a pass rush generator (basically capitalizing on the fact that we're in a pass dominant league). So, in a four wide formation, this makes MUCH more sense.
Those big tackles are now being asked to come all the way out from that 4 gap to the 9 in order to stop the rusher. So basically, you have a mismatch of the end's speed versus the tackle's size. Speed will usually win so you pretty much a have clean easy shot at the quarterback every time. The obvious weakness is against the run. But, as mentioned, if you have size at the tackle position and solid linebackers, that doesn't matter.