I agree with Kitsie, that's what I was going to suggest. Check your needle plate to see how big the hole is. The needle plate is the metal piece between your needle and the bobbin, the needle will dip down into the hole as your machine sews. It sounds as if the needle is dragging your fabric down with it. Holding thread tails, using leaders & enders will work, but I found using a needle plate with a small round hole instead of a wide oval hole was the simplest fix. Also, make sure you're using a sharp needle such as a topstitch needle and not a ball point (which is for knits).
Hope these tips work for you! Good luck!