Short answer; no, I would not suggest using percentage for weights.

Long answer; Please considering what the weight value expresses. It is not necessarily a value chosen by a typographer. It should be the measured thickness of the dominant strokes of a font. If my assertion is correct (which I admit can be debated) then it would make sense to keep the values between 0 and 999. For example, if the dominant stroke width is 123 design units (e.g. the thickness of a lower case 'l')  then the weight should really be 123 and not 100 or "light". Although the weight should be a measured values from the font, I do think it is often a value chosen by the font designer, or possibly rounded to either 400 or 700 in some cases. Then again, I don't see any problems in normalizing these values to a percentage (related to the design units per em of the font). It already is a value relative to one thousand (an em of 1000 design units), so changing it to percent  (relative one hundred) would not cause any problems (nor any benefits).

You could also specify weight as "bolder" and "lighter", which one could define as a percentage. I would like to avoid this and simply deprecate that use (relative weights). You can't really depend on the ability to create fonts with a synthetic weight (e.g. MM fonts), nor do I like the result I get from using relative weights to select next/previous weights of a font family (inconsistent result on platforms with different set of fonts).  Text that should be bold, normal or light easily get too bold or light or not enough bold or light with computed relative weights as well. For pages where fine typography is not needed, then "400" and "700" would be enough to use bold and non-bold fonts. For pages with fine typography, you would want to be able to select a known font without any possibility of ambiguity, i.e. with an explicit weight value that matches the (web-)font exactly. In either case, you don't need "bolder" and "lighter".
Em2 Solutions AB
Michael Jansson

Dylan Just wrote:
As such, I would be all for a proposal to define the font-weight
values to include numeric values (0-999).

What about a percentage value, instead?