It seems to me that weight preference in razors is mostly a matter of personal preference. For regular razors, which cut by compressive force, a good amount of head mass does seem to help drive the cutting edge (cf. the fairly massive head of the iKon S3S, a very smooth cutting razor). [update: Note that if the razor's head is heavy, the handle must also be heavy to avoid an awkward, head-heavy balance. /update] Absent head mass, you have to provide the cutting force without that assistance, but it seems to work just as well, just a somewhat different feel in the hand—the Dorco PL-602 is an excellent razor of very light weight, and I get excellent shaves from it (and to be clear, a shave is "excellent" for me if it is both enjoyable and efficient, easily leaving a smooth finish.
With slants, I find it's somewhat a different story. I am one who finds that a slant encounters noticeably less cutting resistance than a regular razor, so head mass is not an issue. Moreover, very light pressure on the face seems to be much more important with a slant than with a regular razor (partly because slants do cut more easily). The very light weight of plastic slants is thus less of an issue than with regular razors, and some plastic slants (the vintage Merkur white bakelite slant, the Fine Superlite, the Phoenix Artisan Bakelite slant) work quite well even with the light weight. The light weight of the razor can serve as a reminder to use very light pressure against the skin.
But different people often have different preferences.