For an example, let's talk about lifting weights. When you lift weights (or do any exercise meant to make you stronger) you aren't just making thicker muscle cells. You are literally ripping your muscle cells (tiny rips, but still rips) when you work out, then letting them heal over. Everyone used to think that the pain you felt after a workout was your lactic acid buildup after anaerobic respiration, but the more we learn about lactic acid, the more we doubt that. See, lactic acid is awesome. It builds up, yeah, but as soon as you start getting enough oxygen again it will turn back into pyruvate, which we can put through aerobic respiration to get some sweet, sweet adenosine triphosphate (molecular energy, if you will). Tears can't transform and be recycled; tears just hurt for a bit until they heal over. Hence the days of pain after especially hard workouts. So the pain of a workout is not weakness leaving the body, it's your body becoming brutally aware of its weaknesses.
What about the pain of loss? To keep things light, we'll use a hypothetical situation in which I steal a candy bar that The Man was saving for a hard day. The pain is not weakness leaving him; it's him realizing that he is weak because he has trouble living without his candy bar.
The pain of being fired? Realizing that you are weak without an income. The pain of getting blisters on the bottom of your foot? Realizing that you are weak because you are not a hobbit. The pain of hemorrhoids? Uh...let's stop there.
I also think I don't like that phrase because it implies that weakness is a bad thing and needs to be gotten rid of. We need to be hard, unfeeling, and apathetic. I disagree. I think we need weaknesses.
I need weaknesses to keep me humble. Maybe you need weaknesses to keep you kind. Weaknesses shape us just as much as strengths do. Now, one could always make the counter-point that some weaknesses should be gotten rid of, like cowardice or greed, and I wholeheartedly agree. However, not all weaknesses are bad. Just something to chew on. Now get the computer out of your mouth. Gross.