Is it healthy to be overweight?

It's not always UNhealthy, depending on how much overweight, where one carries the weight, etc. It's not typically advisable, but the human body can handle being more pounds overweight (in general) than underweight. You may see people hundreds of pounds overweight, but it's not possible to even achieve "hundreds" of pounds underweight. 

It is considered unhealthy to be more than 10% above or below your healthy weight range.

I might eat fast food for 5 days and weigh 300 lbs.

Being overweight doesn't instantly mean you're unhealthy - you can also be underweight and unhealthy. It depends more on lifestyle and fitness than BMI / weight alone