I've been looking into the legality of it.  Fat isn't a protected class, so it's no hate crime, and it's not harassment if you are handed a flyer in public you don't agree with.  However, it's illegal to impersonate a limited company (calling yourself LTD is fraud). And I think they needed permission to distribute any leaflet on the tfl network, which I don't think they had (and why leaflets are given on pavements primarily).