I am 14 years old I am 5 foot 6 in height and 178 pounds in weight Am I overweight or at a healthy weight?

You are fine. According to BMI charts, 5' 2" people of your age shouldn't weigh more than about 135 pounds. But even then you don't necessarily have to loose weight. Everybody's body is different. As long as you're a fairly active person you shouldn't worry about what a scale says. Now, I know you don't have to loose weight, but if you just want to put on a little more muscle that's fine. Start out small, maybe go for a 20 minute walk after your homework is done. But you are definitely NOT FAT!