Varying thickness line with curve attractor

I’m trying to make a sequence of concentric circles with variable thickness that is controlled by an attractor curve (multiple curves actually).

This is the desired effect:

The problem I’m having is with defining falloff. I want the thickness to increase in the close proximity of the curve and stay constant when far away (thin line).

I tried to achieve this with lofting perpendicular lines of varying lengths, but the falloff is to gradual.

Am I going in the right direction here? Is there a better way of doing this.
I’ve attached the gh and rhino files. circles (13.2 KB)
circles.3dm (34.5 KB)

Thank you for reading, cheers!


Hope this helps you out. Best.

circles (480.4 KB)


Thank you so much! I’m gonna pick through this file to learn something.