There are many advantages to using solid backing for arching in stone arch bridge construction.
The “backing” is the fill or other material placed against the outside of an arch on the inside of a bridge. The backing may simply be fill such as dirt or gravel. Large rocks thrown in are better than just loose fill. However, the best backing is solid masonry or concrete.
Why Solid Backing Strengthens Bridges
To understand better what backing does, consider the case of a free-standing Roman arch. The weakness in a Roman arch is in the haunches. If enough weight is placed on top of the arch or if the arch ring is too thin, the haunches bulge out and the arch will collapse.
Adding weight above the haunches will tend to hinder them from bulging out. This is what the backing does. It stabilizes the bridge by forcing the arch stones together. If this backing is dirt or something loose, individual stones can work their way up into it. However, if the backing is large masses of solid material like stone or concrete, it is extremely difficult for arch stones to ever work into it.
The upshot is the bridge becomes a large, unified mass.

Solid Backing at Work
Not surprisingly, stone bridges with solid backing are much stronger than ones with loose material poured atop.
As an experiment, you can build a small arch out of a single width and thickness of small, random uncut stones. The completed arch is apt to be quite wobbly, and weak.
Adding more stones up against the arch, however, will strengthen it noticeably. This shows what backing does. It stabilizes a bridge.
Solid backing helps compensate for imperfections in the arch. This is a helpful thing to remember for DIY projects. Even bridges with perfectly cut arch stones can handle more weight if provided with solid backing. This is because extra-heavy loads are much less able to cause movement in the arch.
Finally, solid backing does not wash out or get waterlogged easily. There is less strain on the spandrel walls than there will be with loose soil thrown into the bridge. The advantages of this type of construction are many.