How a bobbin is wound does affect the stitching a lot. With the tension too tight, my bet is that the thread stretched as it was loading onto the bobbin. When you went to sew with it, the thread was already stretched so much it had no "give" left for the stitching action.
Sloppily-wound bobbins typically have a different problem -- you get bird's nests underneath! You might want to try out the new bobbin on a test piece to make sure the tension on the bobbin winder is correct now.