If you have a projectile and you double its mass, how would this affect its horizontal velocity?

Its horizontal velocity is determined at the instant of launch ... the angle and speed with which you launch it.  

I suppose its mass might have some influence on how fast and at what angle you launch it, but we'd have to know more about how strong you are, and how you throw, to know what the effect of the mass might be.

But that's still just the effect the mass has on YOUR ability to handle it.  If we can assume that you launch every projectile at the same angle and with the same speed, then their different masses have no effect on their range.  Every projectile you launch hits the ground at the same place.  Mass makes no difference.