Florida, like most states, defines deadly force as force that is likely to cause death or great bodily harm. This doesn't require that a deadly weapon be present, but it ultimately does require that the victim reasonably believe that their life was in danger. A 4'10" twelve year old could reasonably believe that a 6'2" twenty-five year old would pose a threat to their life without a weapon (assuming that the twenty-five year old has physically done something to cause such a belief), but the opposite would likely not be deemed reasonable.
Usually the question of reasonableness is decided in a court of law, which is why some people are upset. Especially in a situation like this where the police apparently have very little evidence which corroborates Zimmerman's story, other than injuries which did not require hospitalization, and "witnesses" who didn't actually see the attack.
Zimmerman may be in the right, or he may be in the wrong, but it probably should be tried in court due to lingering questions which police investigations have been unable to definitively answer.
*EDIT: Also wanted to add that Florida law allows you to use deadly force not only in response to deadly force, but to prevent a forcible felony (rape, robbery, kidnapping, etc.). This is another "out" for Zimmerman, but it still comes down to the question of reasonableness: Given all of the known facts of the situation, would your "average" person have a reasonable belief that Trayvon was attempting a forcible felony? If yes, then the use of deadly force in self defense was proper. If no, then the use of deadly force in self defense was improper.