Why Are We So Weak in Dreams?

When we are in REM sleep (where dreaming takes place) our brain turns off all motor functions. This state is called nonreciprocal flaccid paralysis. This is useful to us so that we can be motionless while we sleep and dream, and not "act out" our dreams.

Why do my legs stop working in my dreams?

Dream legs often tend to represent the dreamer's underlying sense of self-confidence or level of 'supportedness' that she feels in the world. In your dream though you are stuck. You just can't seem to get anywhere and I suspect this is directly connected to something in your emotional or waking life.

Why can't I run fast in my dream?

To dream that you are trying to run but cannot make your feet move as fast as you want them to, signifies lack of self-esteem and self-confidence. It may also reflect your actual state of REM paralysis while in the dream state.