We're asked to weaken the argument, so let's identify what it is!
Conclusion: The first Eurasian settlers to North America probably came from a distant part.
Why?: Because a mastodon skeleton from that time period was found in North America with an arrowhead that is different from any found in the near part of Eurasia.
(Excuse the shift from "projectile" to "arrowhead," but a man's got to grasp these arguments quick!)
So, what's the gap? This problem, in a subtle way, presents a false dichotomy. It assumes that the settlers must have been either from a near part of Eurasia, or a far part. Perhaps they came from somewhere else entirely (I know, they'd probably have to cross through Eurasia, but...). Another issue is that perhaps the arrowhead is one that's used in the near parts of Eurasia, but we never found any evidence.
The answer, (A), capitalizes on these gaps. If the arrowhead found in the mastodon doesn't match any arrowhead found in Eurasia in that time period, then perhaps it came from some other place, or, perhaps the archeological record is inconclusive.
(B) is out of scope. The folks in the near part of Eurasia being nomadic doesn't tell us anything about the connection between the evidence and conclusion. It's tempting if you think "well maybe those folks moved to a far away part, got a new type of arrowhead, and then moved over to North America." But that's a lot of ifs! If you have to do that much work to make an answer choice weaken, it's probably wrong.
(C) is a premise booster. We already know about the arrowheads!
(D) is out of scope. Knowing that there are other artifacts in common between the near and far groups in Eurasia is irrelevant. So what if they both have the same taste in hats?
(E) contains a subtle detail creep. It discusses the conditions before the Ice Age, but we're interested in the time shortly before the peak. More importantly to our understanding of weaken questions, knowing that North America is nicer than the close parts of Eurasia doesn't disconnect the premise and conclusion. It simply says that there would be a reason for those people to move, but we still can make our argument about the arrowheads.