Many people find themselves falling in love when they are weak, sick, or mentally ill, because ever person searches for someone to take care of them and wants to know that there is someone out there that cares about them enough to take time out of their day in order to help them.
When you are stronger and more stable, you're more likely to be selective about what feelings you go through. When you're weakened, it's that much more probable that a sensation like love, easy to fall into and obsessive when it occurs, will happen in your life. While love =/= weakness, it seems to happen more when you feel in need of something.
Not sure if this is reference to real life or movies, maybe both, either way I do not notice the trend. Most people fall in love when they meet someone they can along with. They give them a chance because they have something in common or enjoy one anothers company and it ends up being more than they expected.