Generating Bezier curves/splines that have consistent variable distance from generating function

Question

Is there any way to generate two Bezier curves (or splines) that are a variable but consistent distance away on both sides normal to the curve, based on weights provided at each endpoint? Is it also possible to do this with different forms of easing, i.e. linear, quartic, cubic, or potentially a spline generating-curve?

Here is a mockup I made with Inkscape, the red curve is the base curve, and the black curves are the ones that would be generated. (not perfect)

Ideally this could then be used to export svg shapes with those outlines.

To be clear, I am not looking for a way to generate discrete points a distance away from the curve. I am looking for a way I generate a curve or spline.