Chubby is just a general term, obesity is a medical term. Obesity is when someone has surpassed the recommended average weight for there height and age.
Obesity is when you are excessively overweight, more than 25 per cent over your ideal weight. Chubby is when you are pleasingly plump or have a rounded shape.
If one is chubby, one may be visibly overweight, but not have a BMI (Body Mass Index) exceeding 30--the marker of obesity. Obesity is considered far more unhealthy and dangerous.
The definition of obesity is to have an excess amount of fat. Doctors often refer to patients as overweight, mildly obese or obese. Chubby is often not as severe as the term obese (and not as scientific).