Regular ball-point pens are not acid-free, and being oil-based, after time they soak through the paper and spread. I've had photos which people have written on the backs of in ball-point pen, showing the writing through on the picture, ruining it. Such a shame.
Faber Castell make an extremely fine fibre-tip for micro-writing. I think it is marked as S for Superfine, then F for Fine which is thicker, then M for Medium, and B for Brush is the thickest. I have those in black and brown.
Making a very fine white pen would be a nightmare, since the pigment that makes it white is thicker than the darker colours. I would love to have one of those too.