Anomalously large linear and quadratic Zeeman shifts are measured for weakly bound
ultracold Sr288 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 ab initio model.