Start with baby animals. They're small and fluffy, but surely part of the appeal is their vulnerability. My fat, old cat was once a teeny kitten small enough to hold in the palm of your hand. I can remember feeling her little heart pounding against my palm as she met the dog for the first time. The dog - then an exuberant 2 year old Border Collie - must have seemed a giant to her wide eyes.
And what did that terrified scrap of tabby fur do? Hissed, and spat and fluffed up her bottlebrush tail. The dog could have killed her with one snap of his jaws, but she was having none of it. Vulnerability, combined with a lack of awareness of the vulnerability is surely a large part of the appeal of baby animals. The fluffy chick doesn't think it's cute, it just sets off to scratch more dirt. The floppy eared puppy scampers around the bigger dogs, oblivious to the potential danger. And this transfers to people. Tiny Tim in A Christmas Carol - a character defined by vulnerability - is not self-pitying but resilient.
From the reverse angle, there's something very appealing about strong characters having a vulnerable spot (a bit like the Athena poster of a muscle-bound bloke cuddling a newborn baby, which was nearly as popular as the tennis girl with no knickers). That moment when the tough commander breaks down, or the stern head teacher softens and reveals their human side is a film cliche, but memorable moments are made from the strong showing their vulnerability.
One of my favourite books as a child was Children on the Oregon Trail by A. Rutgers Van Der Loeff, and my favourite bit (which still has me welling up just thinking about it) is the scene at the end when John, who has shown such strength of character to get himself and his 6 younger siblings across the mountain passes on their own after his parents die, breaks down and reveals that despite all this, he is still just a child. Strong, but vulnerable. Vulnerable but strong. Gets me every time.