Originally posted by Michael Piziak I have a 1 gallon jug of water hanging from the tripod for weight
That should help with vibration, but if it's swinging in any way that could also be the source of problems.
As a rule I tend to shoot on a 2 second timer and move back from the camera each shot, so would be likely to see any disturbance at the start of the shot.
ProfessorBuzz's suggestion of tripod sag seems a good place to look too.
A quick measurement of the length of the tick relative to length of star trail should give you a good guide to duration of this effect which may help with diagnosis