Does the same issue happen using two plain fabrics?
Does the issue happen with a sample size quilt sandwich? (Two layers of fabric with batting)
Try to lengthen and/or widen the zig zag setting. Sometimes the setting is too close together and adding extra thickness just won't work.
As mentioned above, investigate the correct needle/type for the project.
Last tip: Re-thread the machine to make sure the thread is caught in all the tension places correctly.