  We deform a defect conformal field theory by an exactly marginal bulk
operator and we consider the dependence on the marginal coupling of flat and
spherical defect expectation values. For even dimensional spherical defects we
find a logarithmic divergence which can be related to a $a$-type defect anomaly
coefficient. This coefficient, for defect theories, is not invariant on the
conformal manifold and its dependence on the coupling is controlled to all
orders by the one-point function of the associated exactly marginal operator.
For odd-dimensional defects, the flat and spherical case exhibit different
qualitative behaviors, generalizing to arbitrary dimensions the line-circle
anomaly of superconformal Wilson loops. Our results also imply a non-trivial
coupling dependence for the recently proposed defect $C$-function. We finally
apply our general result to a few specific examples, including superconformal
Wilson loops and R\'enyi entropy.
