How do I change the line width of an arrowhead to match its line segment?

I have drawn a line segment of width 0.5 pt and added Arrowhead 1 (a simple V-like arrowhead) to an end of it.  However, the arrowhead that appears has a line width of 1 pt, and indeed seems to have this line width regardless of the width of the line segment.  How do I change the arrowhead line thickness to match the line segment width?  (I need to make hundreds of these arrows with different line widths and so would prefer a solution that scales well.)  Thanks.

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UPDATE:  As one attempted workaround, I thought perhaps I could build the artwork at a scale at which all arrow line segments are naturally 1 pt wide, then select "Scale with object" for all line segments, and scale down the artwork as a whole by 50%.  However this also doesn't work -- see the screenshot below.  (I achieved the "Want" line below by applying "Convert Outline to Object" to the arrow, but I do need to keep the arrows as outlines rather than convert them to objects.)

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