Right now, the default width is being based upon the image size, which by the looks of it, is probably 36wide, by 48 pixels wide
for example, I made an outline of whats happening
You can see the bounding box and why he is doing that.
What you need to do, is set probably defaultWidth/2 and then offset it a bit to be centered
So it looks and behaves more like
many games do support a 'stand on ledge' by 1 pixel type approach
megaman for example
As you can see here, the bounding box is slightly smaller than the character, and his feet overlap the ground tile
However somegames actually use a combination box AND a 'circle' for the character. (box for left/right and top collsion) but then a circle for feet, so they can stand really close to the edge. But because of the 'roundness' of the circle. They could potentially slide off the edge.
However there are many approaches.
I would suggest looking at this site, it has some good informationhttp://www.emanueleferonato.com/2012/05/24/the-guide-to-implementing-2d-platformers/