Inducing magnetism in graphene holds great promises, such as controlling the exchange interaction with a gate electrode, and generating exotic magnetic phases. Coating graphene with magnetic molecules or atoms has so far mostly led to decreased graphene mobility. In the present work, we show that Pt-porphyrin molecules adsorbed on graphene lead both to an enhanced mobility, and to gate-dependent magnetism. We report that porphyrins can act both as donor or acceptor molecules, depending on the initial doping of the graphene sheet. The porphyrins transfer charge and ionize around the charged impurities on graphene, and, consequently, the graphene doping is decreased and its mobility is enhanced. In addition, ionized porphyrin molecules carry a magnetic moment. Using the sensitivity of mesoscopic transport to magnetism, in particular, the superconducting proximity effect and conductance fluctuations, we explore the magnetic order induced in graphene by the interacting magnetic moments of the ionized porphyrin molecules. Among the signatures of magnetism, we find two-terminal-magnetoresistance fluctuations with an odd component, a telltale sign of time-reversal symmetry breaking at zero field, which does not exist in uncoated graphene samples. When graphene is connected to superconducting electrodes, the induced magnetism leads to a gate-voltage-dependent suppression of the supercurrent, modified magnetic interference patterns, and gate-voltage-dependent magnetic hysteresis. The magnetic signatures are greatest for long superconductor/graphene/superconductor junctions, and for samples with the highest initial doping, compatible with a greater number of ionized, and thus magnetic porphyrin molecules. Our findings suggest that long-range (of the order of the coherence length, or micrometers) magnetism is induced through graphene by the ionized porphyrins' magnetic moment. This magnetic interaction is controled by the density of carriers in graphene, a tunability that could be exploited in spintronic applications.