3 questions that come to mind is...
what size & type of thread are you using in the top and what size needle are you using?
If the needle you are using does not pierce the fabric with a large enough hole to accomadate the top thread, the bobbin thread will continue to come to the top every time. 80/12 is the size I use most but depending on the thread or fabric, I may even move up to a 90/14.
Also, most embroidery threads are 40 wt and I have found with my machine that I have to loosen the top tension to atleast a 3.0 and sometimes all the way to 2.0 depending on the fabric and the thread. It usually doesn't take long for me to notice when I miss this step.
Stablizer is to keep the fabric stablized from puckering and should not have anything to do with your bobbin thread coming thru the top.
Hope this helps, Linda