Lets look at some passages where the term is being used:
"we also retain what one might call laws of metaphysics. (Despite the grand name, no heavy-duty metaphysics is intended; the underlying account of lawhood is reductive.)" (Theodore Sider, Writing the Book of the World, 2012)
"Those pursuing [the project of providing a metaphysical account of causation] think it important to provide a metaphysics for causal claims or to specify what causation 'is', metaphysically speaking, or what the metaphysical 'truth-makers' or 'grounds' for causal claims are. Those committed to this enterprise sometimes invoke heavy-duty metaphysics involving relations of necessitation between universals, dispositional essences, and the like, although others prefer sparser, more 'Humean' candidates for truth-makers" (James Woodward, A Functional Account of Causation, 2014)In both of these passages "heavy-duty" is just equivalent to "ontologically excessive". If an account is reductive or is committed to a sparse ontology, then it is not heavy-duty.
Sometimes the assurance of no heavy-duty metaphysics being involved indicates that the account is intuitive or commonsensical:
"To appreciate the exclusion problem, we do not require much heavy-duty metaphysics - overarching doctrines about mental anomalism, "strict laws" in causal relations, a physical/mental conception of causality, token physicalism, and the rest. It arises from the very notion of causal explanation and what strikes me as a perfectly intuitive and ordinary understanding of the causal relation." (Kim, Mind in a Physical World, 2000)
"Nearly all the philosophy we have looked at so far begins from what are relatively ordinary, everyday considerations. ... Hegel's thought in the Philosophy of History, in contrast, arises out a grand vision of reality and the forces that move it - this is heavy-duty metaphysics." (Edward Craig, Philosophy: A Very Short Introduction, 2002)This sense is clearly different from the previous one. After all, it is not as if Humean or reductive metaphysics is part of common sense.
I see nothing wrong with doing heavy-duty metaphysics in either of these senses. First, there is no reason to think that the deep nature of reality matches common sense or that folk metaphysics is even coherent. Science, especially contemporary physics, often goes directly against common sense, and unintuitive theories become accepted by the scientific community. If a metaphysical theory is weird, then the theorist can just provide reasons for her claims, unapologetically. There is no reason to even start from "ordinary, everyday considerations", and it is perfectly fine to have a fully fleshed-out metaphysics in mind when formulating a problem.
Eric Schwitzgebel thinks that the true metaphysics of mind is inevitably going to be "crazy" because none of the major views are thoroughly commonsensical, even when the theorists take common sense as their starting point:
"I believe that there is not a single broad-ranging exploration of the fundamental issues of metaphysics that doesn't, by the end, entangle its author in seeming absurdities. Rejection of these seeming absurdities then becomes the common-sense starting point of a new round of metaphysics, by other philosophers, which in turn generates a complementary bestiary of metaphysical strangeness. Thus are philosophers happily employed." (The Crazyist Metaphysics of Mind, 2014)
Second, a metaphysical theory should not be favored just because it is sparser, although I am a fan of Ockham's razor. Sometimes ontological sparseness has a cost in terms of a loss in ideological economy (the number of primitive predicates) or explanatory power (I, for one, think that the existence of regularities must be explained). It is not even obvious that a Humean metaphysics is ontologically sparser since it is often taken to be committed to the existence of quiddities.
Most importantly, it is all just more metaphysics. Humean and non-Humean accounts are both metaphysical pictures of reality. Both are highly speculative and require lots of theoretical work using traditional a priori methods. So, in both cases, there is something "heavy-duty" going on. And prima facie, both are equally valid candidates. So there is no reason to apologize for developing and defending either account. If we want to understand what lawhood or causation really is, we have to develop both frameworks side by side until we finally reach the truth.
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