The key to weakening an argument in critical reasoning is finding a flaw in the argument and exploiting it.
For example, if the premises for an argument state that a test on college aged students had a specific result and then the conclusion is based on the general population, we know that the correct answer will likely exploit this flaw.
For example, it might say something like, “college aged students tend to have perform differently than people in their mid-twenties and older.” The correct answer is to weaken question is rarely something like “many of the scientist theories have since been discredited,” etc.
What the GMAT is really testing is your reasoning skills, so the best thing to do is to help sever the connection between the premise and the conclusions, making the argument less logically reasonable.
So what is the correct process for Critical Reasoning weaken questions?
Like all CR questions, you must first read the question. Seeing that it is a weaken question, you should then search for missing links between the premises and the conclusions. Make a note of these missing links in your head, so you can keep them in mind as you go over the answer choices. Eliminate anything that is irrelevant or out of scope and pick the answer that does the best job of weakening the connection between the premises and the conclusions.