Are you machine stitching the binding down?
It may be easier for you to use something like "Steam a Seam 2" to hold the binding in place while you work with the quilt to manipulate it around your machine. I've found I get stuck a lot using pins, and clips have a tendency to maneuver themselves loose when working on a large quilt.
Yes those quilts are heavy, especially if using an old blanket as the lining. I sew all my quilts on my little Singer Featherweight and without that support to the left of the machine (both in front and behind the machine) I can not get enough of the quilt in front of and behind the needle to get the binding on straight.
These ideas work with some degree of practice. I do a number of charity quilts in larger sizes in order to get my skill level up (and keep it up) while working with larger materials in my small machine.
Good luck! We look forward to hearing how it goes.