These movements are secondary parts of stuttering that many people develop over time as a result of the psychological 'layers' that build up over time. Usually people try 'tricks' (either consciously or not) to avoid stuttering or to release the tension they feel. Might help at first but then becomes less helpful over time, then you might try another 'trick' and that's how it continues. The underlying reason is avoidance of stuttering. Sometimes the struggle becomes bigger than the stutter itself.