First thing I would check would be the tiller. This is the distance from the base of the limb (where it meets the riser) to the string. This measurement is taken at a 90 degree angle to the string. It should be exactly the same on the top and bottom limbs.

If the bottom limb were cranked down more than the top it might cause the problem you described. Adjustment to tiller is made by cranking the limb bolts in or out accordingly.

I don't know what type of bow you have, but a two cam bow that is out of time may cause this. Most new bows do not need a stabilizer. They hardly move in your hand when shot. If the bow is properly tuned and the problem still exists you may want to go ahead and try a heavier stabilizer. I don't think your form is the problem.