In most cases, your family might be right. I'm assuming nothing about how you lost the weight (healthy or unhealthy loss). Of course, if you just dropped 5 pounds, then your family said that, it might be unreasonable worries. However, if you lost a considerable amount in a short period of time (like 40-50 pounds), then the worry might have some validation to it.
Ask what their concerns are. In some cases, the new appearance might make them feel uncomfortable. However, if you're continuing to drop the weight, then you might want to consider their concerns. There is nothign wrong with dropping 40-50 pounds, but if you drop below your natural body weight, you may end up with problems.