You need to ensure that the thread is going from the thread spool at the back of the machine, through the eyelet, then around the silver tension disc on top of the machine, then to the bobbin when you are winding it. Also, pull the thread tail up through the hole in your bobbin to start and hold the tail so the thread starts to fill smoothly and doesn't loosen.

I've marked the disc in red on this image

Please read my Tip on bobbin winding; its really important to get a good wind and you can add more tension yourself by applying gentle pressure to your thread spool on the back pin as you wind off it.
Link is http://www.fixya.com/support/r10598580-winding_bobbin_correctly

The stopping when full is possibly because your bobbin is winding unevenly but I never run it until it stops itself anyway, and do the winding at 3/4 speed, not flat out. You want a really smoothly tensioned even wind onto the bobbin so your thread comes off the bobbin when stitching with even tension, not stretched, then loose.

Hope this helps you with your problem.