Are you supporting the weight of the quilt while you are stitching so that it isn't pulling backwards? I throw mine over my shoulder so that it lets the pressure foot do all the work. And, still, I am ready to help push or pull a little bit if necessary. If you find this is your problem, there was a wonderful do-it-yourself project made of PVC pipe that supports the weight of the quilt for you.
http://www.quiltingboard.com/tutoria...e-t250308.html
Does your foot have a way to adjust the pressure? Ironically, on my older Singer, if I had very fine material I had to use a very light pressure, but with a heavier item...think denim, back then I wasn't quilting...I had to increase the pressure.
When you say Singer Quilting machine, do you have a model number? Do you have the manual? Could we see a picture of the machine and how you quilt? A lot of the quilting machines are mostly for piecing, but should be able to quilt the pieced top.
Edited to add: I reread your post and realized you said the thread was puckered on the back. Does that mean the bottom thread is almost straight so that the top thread is sorta looped around the straight bottom thread? If this is the case, you may have a problem with the thread hanging up on your bobbin. Or your bobbin pressure is too tight. Or that the top thread is not threaded right through the tensioners causing the bottom to be too tight. I would love to see a picture of the stitching, both top and bottom. Does your regular piecing stitch look normal?