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We report a polarized neutron diffraction study conducted to reveal the nature of the weak ferromagnetic moment in the superconducting ferromagnet UCoGe. We find that the ordered moment in the normal phase in low magnetic fields (B // c) is predominantly located at the U atom and has a magnitude of about 0.1 muB at 3 T, in agreement with bulk magnetization data. By increasing the magnetic field the U moment grows to about 0.3 muB in 12 T and most remarkably, induces a substantial moment (about 0.2 muB) on the Co atom directed antiparallel to the U moment. The anomalous polarizability of the Co 3d orbitals is unique among uranium intermetallics and might reflect the proximity to a magnetic quantum critical point of UCoGe in zero field.