  Anomalously large linear and quadratic Zeeman shifts are measured for weakly
bound ultracold $^{88}$Sr$_2$ molecules near the intercombination-line
asymptote. Nonadiabatic Coriolis coupling and the nature of long-range
molecular potentials explain how this effect arises and scales roughly
cubically with the size of the molecule. The linear shifts yield nonadiabatic
mixing angles of the molecular states. The quadratic shifts are sensitive to
nearby opposite $f$-parity states and exhibit fourth-order corrections,
providing a stringent test of a state-of-the-art \textit{ab initio} model.
