Pete Riegel is smiling from above to see someone conducting and reporting on experiments in this forum. Thanks Oscar.
Like most people I'm guessing, I tension the tape by feel when measuring a cal course. I do occasionally get my fish scale out to check what 10-11lbf feels like though, just as kind of an ad-hoc calibration. I think there is a tendency to pull harder that you should, so it's a good idea to check yourself every now and then.
The stretch of the tape should be linear as a function of pull force. The fact that your data does not show this just indicates it's hard to be precise with this, and there is going to be some scatter. The hope, which I think is justified, is that the scatter of multiple tape pulls will tend to cancel itself out.