Weakly non-linear Marangoni convection in a horizontal layer of an electrically conducting fluid heated from below and submitted to a uniform vertical magnetic field is investigated. The influence of the strength of the magnetic field on the nature of the convective patterns and their stability is analyzed by using the amplitude method. To examine the role of the thermal properties of the lower rigid boundaries, two different situations are, respectively, treated, namely a perfectly heat conducting and an adiabatically isolated wall. The presence of a subcritical region whose area generally decreases with the magnetic field is displayed.