Keep line renderer width same on screen no matter camera distance

I assume you really do mean "line renderer" when you say "line renderer" - I'm not sure you could do this with a trail renderer.

I don't think there's an "easy" mathematical trick, unless your camera movements are going to be very limited. You might consider scaling the width based on the camera's distance from the scene origin (the sun?). Depending on how your camera can move, this may satisfy the request.

 scale = $$anonymous$$athf.Lerp(min, max, distanceBetweenCameraAndOrigin / maximumDistanceConsidered);

To achieve truly perspective-independent width, you'll need to programmatically create your lines from multiple dynamically-billboarded quad segments and size them in a way that respects each vertex's position in screen space. This is not something I've ever had to do, but I've done some work in the general area; it's not for the faint of heart. ;)