I don't care that I weigh some multiple of an SI unit, or some fraction of a car. I care about my weight relative to others and my history.
What instrument do you have that measures your "weight relative to others and your history"? Don't you only want to measure it relative to other healthy individuals? And, if you are particularly underweight or overweight, wouldn't you want to know when you're in the normal range? An instrument that only tells you what direction the change is doesn't tell you any of that.
That’s an edge case. People who fall in that category already know that. And they’re very interested in their accurate, absolute weight.
Besides, BMI is just a convenient way of quantifying what a “healthy weight range” is. I could have used any range and said I was interested in weighing between X and Y.