"Perceived weakness" refers to a weakness or flaw that is not necessarily true, but is believed or seen by others. It is how someone thinks you are weak, even if you may not truly be weak in that aspect.
His bill would allow teachers — if they want — to address perceived weaknesses in evolution studies in the classroom. (utahpubliceducation.org)
Some of the division is about policy but much is over perceived weaknesses in leadership, management and communication. (theconversation.com)
Now think about what separates you from your competition, how perceived weaknesses may actually be assets, and how you can improve upon your pre-existing skill set. (realtormag.realtor.org)