I got this badge last week (happily gone now), and I just saw SofaJockey turning it down.
I don't understand what this badge is for.
For one, I don't think healthy BMI is a real thing. There are unhealthy BMIs, outside the recommended ranges, but just because you are in the range doesn't mean you are at a healthy weight for your body. At my height 168cm/5'6", the range is 18kg, or nearly 3 stone. I do not believe someone is at a healthy weight at one weight, and still healthy 18kg heavier/lighter. That's more weight than I have lost so far, and my body has made a drastic change. I doubt making that same drastic change again would be healthy.
So it's meaningless in terms of an individual's weight. Does it have some value in the forum? Not as far as I can tell. The maintainer badge says you have succeeded; the weight lost badges tell people how far you have come. But the healthy BMI? That seems to undermine you. In the week I had it, at least two other members said something to the effect "I wish I was at a healthy BMI". I could no longer contribute, because that badge erased my journey, and I looked like a dilettante.
I am seriously interested in what value the admins see in that badge, because it seems useless to me.