For a policy that's ostensibly designed to fight air pollution and "reclaim streets for pedestrians and cyclists", penalizing vehicle tonnage seems like a weird way of achieving it. If you want to fight air pollution, charging based on emissions like the ULEZ in London[1] seems like a much more effective way of doing so, especially since a 20 year old sedan can easily emit more air pollution than a recent SUV. As for "reclaim[ing] streets for pedestrians and cyclists", the bigger problem is arguably on-street parking itself and the space it occupies, rather than the of the cars occupying them. If you want to create more space for pedestrians and cyclists, replace on-street parking with cycling lanes or sidewalks, and the market (for parking spaces) will take care of the rest.
[1] https://en.wikipedia.org/wiki/Ultra_Low_Emission_Zone