Great questions / follow-ups.
To answer the immediate question, I think that LSAT is fairly consistent about using "reasoning/argument" vs. "claim/conclusion" in the question stem of a Weaken or Strengthen.
The vast majority of these questions say "reasoning/argument", in which case the entire argument core is being evaluated.
For the ones that say "claim / conclusion", I would still be thinking through the core (because I like reliable habits, processes, and tendencies), but technically the correct answer could simply move the needle on the believability of conclusion, without having anything to do with HOW the author got there.
In this example, (D) is specifically about the evidence, about the study. Nonetheless, even without knowing the context of the premise, (D) would still lend credence to the conclusion, since it reinforces a connection between overconfidence and attempting to start a business.
I don't actually notice this "reasoning / argument" vs. "claim / conclusion" distinction when I'm taking the test (only when answering Forum questions).
It doesn't make any difference to my process or evaluation of the answers.
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Another good point that was raised is that this argument is not truly causal in any explicit sense.
The conclusion only makes a statistical claim, not a causal one.
Again, to me, this isn't a super useful or important distinction on this question (which is part of why I went along with the causal language of the original poster ... it's often better to reinforce what's familiar about problems than to carve them up into so many distinctions that it's hard for the brain to latch onto patterns and tendencies).
(D) would be a correct answer whether the question stem said psychologist's "conclusion" or "argument".
(D) would be a correct answer whether the conclusion said "overconfident ppl are more likely to start a business" or "overconfidence makes ppl more likely to start a business".
The weighted average math demonstration was very cool, although I don't think if the Business Managers had an overall confidence level of .85 and the E's had a confidence level of 1 that we could say that the E's overconfidence was "MUCH more" than the BM's.
I also don't think that if 170 out of the 200 subjects have a confidence level of 1 that we would call THEM overconfident. It's more likely that we'd call the 30 ppl who are .5 UNDERconfident. But your mathematical point was still valid, even if 90% of people have NO chance of getting through this problem using that type of thinking.

Despite the lengthy debate on this thread, here are some quick, out of scope features of the wrong answers that are grounds for elimination:
(A) the content of the questions doesn't matter. This does NOT tell us that the subjects were representative of their group title.
(B) It's a super weak statement. And ACCURATELY determining odds is not something the argument needs (they could overestimate or underestimate the odds and still overconfidently start a business).
(C) "Success" is irrelevant.
(E) Actual "business acumen" is irrelevant.