You can use the XML Editor to adjust the scaling and positioning of the arrow head, leaving the stroke width unchanged.

1. Open the XML Editor and find the `svg:defs id`

2. Expand the defs id, and locate the `marker id`, and expand that too, and you will find a `path id`.

3. Select the path ID, click on the Transform property. Type in a new scale value to adjust the size of the arrow head. Press CTRL+Enter to commit the change

4. If the arrow head needs moved, which it probably will if you made the arrow head smaller, click on the `marker id` and change the refX property to move the arrow slightly to one side. Press CTRL+Enter to commit the change

This screen shot shows altering the `marker id` RefX, and the `path id` Transform scale value

[![enter image description here][1]][1]

The beauty of this is that it doesn't break the arrow head functionality of the stroke. You can still edit the stroke, and the arrow head will move as expected.

[![enter image description here][2]][2]

Also, you can use this technique for multiple paths - each marker id, and path id can be adjusted separately.

[![enter image description here][3]][3]


  [1]: https://i.sstatic.net/QjGCS.png
  [2]: https://i.sstatic.net/cny1H.gif
  [3]: https://i.sstatic.net/VMnD6.png