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Excellent question! Yes, you are correct, the statement in (A) could conceivably weaken the main conclusion; however, the question is which answer choice most weakens the argument. If you're faced with two possibilities such as this, try to zero-in on meaningful differences between the two options.
For instance, let's focus for example on strength of language in answer choice (A) versus that of answer choice (B). Answer choice (A) states that many normal weight babies are born to mothers who had inadequate prenatal care. Answer choice (B) states that hospitals routinely classify mothers of underweight babies as ex post facto recipients of inadequate prenatal care. Which of these terms, "many" or "routinely," is stronger? "Many" is a somewhat nebulous term: it could be several (like 40 or 50 out of 500); it could be most (like 300 out of 500); or it could be almost all (like 480 out of 500). In general I tend to lump "many" in with its pal "some," i.e. I treat both like "not none" but don't give them much more rope than that. "Routinely" on the other hand indicates a habitual, fixed program, something that reoccurs with such frequency that it is to some degree unremarkable. Thus, "routinely" is a far more powerful qualifier than is "many" and ipso facto makes (B) a more likely candidate.
As an aside, if I ever come across the word "many" in a strengthen or weaken answer choice, I tend to get very leery of that choice. It's kinda a perennial favorite wrong-answer-word. Not to say it will never appear in a correct answer. It may (and I strongly suspect it has!), but just be aware of what "many" actually means.
In addition, you could ask yourself, "So what if a lot of babies with normal birth weights are born to mothers who received inadequate prenatal care? Does this provide strong evidence against a possible causal link between inadequate prenatal care and lower birth weights?" It all depends on the relative frequency with which underweight vs normal weight babies are born to mothers who received inadequate prenatal care. It is certainly possible that, say, 80% of babies born to mothers who received inadequate prenatal care have normal birth weights. However, even granted the truth of answer choice (A), it is equally plausible that 90% of babies born to mothers who did receive adequate prenatal care have normal birth weights. Thus, even with answer choice (A), we do not have strong evidence against the possibility that inadequate prenatal care could correlate strongly (and perhaps causally) with underweight babies.
Answer choice (B) in contrast gives direct evidence to undermine this link, as you noted correctly. Thus, on its merits, answer choice (B) is a far stronger option and the best possibility when searching for what would most weaken this argument.
Thanks for the great question!