How to model variance of a heteroskedastic dataset

I have a dataset (scatter plot shown below) where x-axis corresponds to observed value and y-axis being the true value (yeah, sort of flipped from the convention where y is the observed value). I am not interested in estimating y per se, but instead, I want to estimate variance of y given x. It might be hard to see from the scatter plot, but the variance of y for bigger x is much larger than x; however, I think that’s simply because the range of x is quiet large. Therefore, even though the variance of y for smaller x is smaller in absolute terms, in relative terms, the variance is much larger for smaller x. I can imagine that one can bin samples by x, and then estimate sample variance of y at each binned level. However, that seems quite ad hoc. I wonder if there is a more principled way to estimate variance of y given x. Also, for practical reasons, sample at certain ranges of x (as you can see from the plot, roughly from x=1200 to x=1500) is sparse. I wonder if this could be taken into account, too.