Via drill layer static dimension in Eagle
It looks to me as if the white drill layer could be used to produce a "drill drawing" with different symbols (various crosses and circles) used to indicate the drill size.  The size of the symbols has no relation to the actual drill size.

Eagle should produce a drill file that will specify the actual drill sizes and hole locations - that will be what the board shop will use when making your board.

(I don't think I've ever produced a drill drawing for any board I've designed.)