Yeah, I'm 'overweight'. I run a lot and generally in pretty good shape. But I could absolutely lose 10-20 lbs of fat. Just because you're a little overweight doesn't mean you're unhealthy.
If you could lose 10-20 lbs of fat (and don't just mean, you have 10-20 lbs of fat left), then tautologically it would be healthier if you did lose the weight. The degree to which it makes you healthier is debatable, but that extra weight isn't making you more healthy (outside of people that are very underweight).