[TLDR] The Resistance for this line is 1.16 lb/ft... maybe[/TLDR]
So, I found some data on generic 'barrier tubing' and decided to extrapolate the resistance of our line in lbs/ft.
Judging from the five points of data given for vinyl tube, it seems that Restriction vs. Size (inner diameter) and Restriction vs. Volume (oz. per linear foot) are best fit with exponential curves. This is sensible given the expected response of a tube approaching 0" ID.
I then applied an exponential fit (with and without X offset) to the three points of data given for barrier tubing and extrapolated for a 3/16" ID tube. Size vs. Restriction yields either 1.30 or 0.87 lb/ft with and without an X offset respectively. Fitting Volume vs. Restriction yields 1.16 lb/ft in both cases.
As the Volume vs. Restriction numbers are more consistent, and are within the range given by Size vs. Restriction, I suggest using the value of 1.16 lb/ft for our calculations.
Now to see how this value compares to reality.
Published data comes from here:
http://www.draughtquality.org/Components-of-Balance
And a little warning about making extrapolations:
http://xkcd.com/605/