Change Default Altium Footprint Part Designator Top Overlay Text Size
In case anyone else found this question, there is a slight change with Altium 18. The Designator now has its own menu:



EDIT: Here is an example of 0.025" text height and 0.005" width silkscreen on a PCB next to some actual components. The resistors are 0603 and the caps are 0402.