My old post on 'Reasons-Talk and Fitting Attitudes' [along with my PQ paper] sets out the basic case for taking fittingness (or fitting reasons, in contrast to either value or value-based reasons) as our sole normative primitive. My follow-up post on state-given "reasons" explains how the fittingness view accommodates the datum that it's more important to (say) prevent the world from exploding than it is to possess fitting attitudes. This importance claim is itself a first-order normative claim that can be understood in terms of fitting attitudes: it's appropriate to prefer, and to care more about, saving the world over having true beliefs (say).
So that addresses one kind of worry that one might have about the normative force of fittingness claims. However, Helen recently drew my attention to another interesting worry in this vein. One might worry that fittingness relations themselves are too "thin", "weak", or lacking in normative "substance" or force. That's fine for the normativity of beliefs and other attitudes, since getting those "right" isn't all that big a deal. But to account for the sheer atrociousness of gratuitous torture, say, using the same kind of metaphysical relation that accounts for the inappropriateness of believing grass to be purple, just seems awfully weak and unsatisfying.
The fittingness theorist can offer a response in two parts. The fittingness relations associated with value are different (from mere fitting beliefs, etc.) in both quantity and quality.
The difference in normative "quality" comes not from the raw status of "being a fittingness relation", but rather from the significance of the attitudes which are thereby warranted. Warranting belief is perhaps a fairly weak kind of normative significance, whereas warranting intense moral outrage is another matter altogether. One misses these important variations in normative significance if all one considers is the relation of warrant, glossing over the crucial question of what response is thereby being warranted.
I think that's the most important point to make. But it's also worth flagging that certain value facts may correspond to a large quantity of fittingness relations. Whereas epistemic evidence calls for a simple belief-response, outcomes of practical importance may call for a wide array of emotional and motivational responses on our part. An atrocity may render fitting various desires, actions, emotions of outrage, despair, regret, etc. etc.
Together, I think this does a pretty satisfying job of addressing the concern. Indeed, I think it's a major advantage of the fittingness view that it makes explicit what the normative significance of value facts is to us. A value primitivist might say, "I see that this is good, but why should I care?" The fittingness view closes off such questions: to be of value just is to be something that merits concern (that it's rational to desire, pursue, etc.). The fittingness view makes explicit how abstract normative facts call for certain psychological responses. So in that way, we should expect it to be particularly well-placed to address objections rooted in psychological or phenomenological concerns (as the above arguably is). Vague metaphorical talk of normative "thinness" or "weakness" aside, what the objection ultimately comes down to, I think, is a challenge to explain why moral outrages are so outrageous. The fact that, on the fittingness view, such moral horrendousness just consists in the situation meriting moral horror and outrage, seems the most direct and straightforward explanation of the datum that one could possibly ask for.