Annika ran a multiband 8 sequence on a GE 3T Discovery MR750 scanner (UCSD CFMRI; TR = 800 msec, mb_factor 8, 32 channel head coil, 2 x 2 x 2 mm voxels; AP - PA encoding directions), and also saw prominent oscillations in the motion regressors, linked to respiration:
the purposeful breath-holding experiment we ran. I was also struck by the size of the oscillations in the movement regressors: somewhere between 0.5 and 1 mm, which neatly matches the size of the larger oscillations we've seen. Annika has results for an awake adult and toddlers, all of whom show oscillations (particularly in the A-P (y) and I-S (z) axes); see this pdf. These comparisons suggest the oscillation magnitude is not directly related to participant weight: the toddler and adult magnitudes are similar, though toddlers of course are smaller and have a faster respiration rate.
Here are some motion regressors Annika collected on a different scanner (Siemens 3T Prisma at Robarts Research Institute, Western University; CMRR release 10b, VD13D, 64 channel head coil, 3 x 3 x 3 mm voxels), at different MB factors. The oscillation is in all runs, though lowest amplitude with MB1.
Finally, here's a set of motion regressors collected on a Trio at MB2 (ipat2 acceleration, 2 mm voxels, TR=1300 msec, AP/PA phase encoding directions, Robarts Research Institute, Western University). Each subplot is a run from a different person. All again have oscillations mostly in the y and z directions, though the magnitude is less than the MB8 plots above.