  Kuwert and Sch\"atzle showed in 2001 that the Willmore flow converges to a
standard round sphere, if the initial energy is small. In this situation, we
prove stability estimates for the barycenter and the quadratic moment of the
surface. Moreover, in codimension one we obtain stability bounds for the
enclosed volume and averaged mean curvature. As direct applications, we recover
a quasi-rigidity estimate due to De Lellis and M\"uller (2006) and an estimate
for the isoperimetric deficit by R\"oger and Sch\"atzle (2012), whose original
proofs used different methods.
