First, let's think about all those layers. Binding is attached as a folded piece, so that's two layers of fabric just into the corner. Then there's the angled fold back, adding two more layers. And another fold at the top, adding yet another two layers. That's SIX layers of fabric right at the corner! And it doesn't all need to be there!
Here's how to reduce that bulk, and cut out four layers of unnecessary fabric. This technique requires the stitching at the corner to go 90 degrees straight back, and not at a 45 degree angle into the corner.
After the binding is all attached, at each corner, fold back the top piece of binding to expose the little triangle underneath.
Fold back the top fabric even more to fully expose that little triangle rascal!
And trim it off, even with the binding stitching.
Ta-da! Four layers of fabric removed!
Now the corners will feel soft and still full, but not thick and stiff. I have done this with my quilts for over a year, and my corners are so much nicer.
So make it a habit - trim your corners! You'll be happy you did!