Binaries harbouring millisecond pulsars enable a unique path to determine neutron star masses: radio pulsations reveal the motion of the neutron star, while that of the companion can be characterised through studies in the optical range. PSR J1012+5307 is a millisecond pulsar in a 14.5-h orbit with a helium-core white dwarf companion. In this work we present the analysis of an optical spectroscopic campaign, where the companion star absorption features reveal one of the lightest known white dwarfs. We determine a white dwarf radial velocity semi-amplitude of K_2 = 218.9 +- 2.2 km/s, which combined with that of the pulsar derived from the precise radio timing, yields a mass ratio of q=10.44+- 0.11. We also attempt to infer the white dwarf mass from observational constraints using new binary evolution models for extremely low-mass white dwarfs, but find that they cannot reproduce all observed parameters simultaneously. In particular, we cannot reconcile the radius predicted from binary evolution with the measurement from the photometric analysis (R_WD=0.047+-0.003 Rsun). Our limited understanding of extremely low-mass white dwarf evolution, which results from binary interaction, therefore comes as the main factor limiting the precision with which we can measure the mass of the white dwarf in this system. Our conservative white dwarf mass estimate of M_WD = 0.165 +- 0.015 Msun, along with the mass ratio enables us to infer a pulsar mass of M_NS = 1.72 +- 0.16 Msun. This value is clearly above the canonical 1.4 Msun, therefore adding PSR J1012+5307 to the growing list of massive millisecond pulsars.
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