How to repair leather belts?
A few thoughts:


If the hole is being destroyed, you may be wearing the belt tighter than the leather will support.  If the belt is otherwise in good shape, you may be able to make a cosmetic repair to the hole, then use the belt at the next looser hole.  
Cosmetic repair: If the leather is torn, try the grommet solution, below, after this repair.  If the hole is just stretched, try pressing it flat, using a tool to push the leather around the hole back into shape.  If needed, use shoe dye or a Magic Marker of the same color to restore color to areas around the hole.  Then apply super glue (thin liquid version) on the backside to saturate the leather around the hole.  Cover both sides of the repair with baking paper (it's silicone treated so the glue won't stick to it), put the repair under a weight, like a heavy book, and leave it overnight.
Functional repair: If you want to continue using the belt at the same hole, there are limited options for a repair that will hold up comparable to the original leather.  That type of buckle typically has a short hook that won't reach through the thickness of an added patch layer on the back.  You need a way to reinforce the hole.

The most practical way to do that is with a grommet.  If the buckle hook is right at the edge of the buckle and the grommet would be exposed and noticeable, you have a couple of choices.  One is to grind away the exposed edge of the grommet head before installing it (you then need to be careful about its orientation when you install it).  Another is to just add grommets to all exposed holes for a uniform appearance (they can be colored to match the belt, but they won't have the dress appearance of plain leather).  

Start with the cosmetic repair described above.  For the grommet going into the damaged hole, augment it with two things.  One is a thin metal washer on the back side.  They may come with the grommets.  If not, cut one from a beverage can (just be sure there are no sharp edges or burs that can damage the trousers).  

The grommet may have a "cupped" head to grab the leather and spread the stress over more than just the hole.  If not, glue the grommet and washer to the leather when installing it (even with a cupped head, it wouldn't hurt to glue the washer to reinforce the leather).  Use a neoprene-based glue like E6000, and wipe off the excess.  Let that dry for a few days (or at least until you can no longer smell the solvent) before using the belt.
That type of buckle typically attaches to the belt via a clamp on the backside.  The clamp pries open and snaps shut.  You can just replace the leather portion with another of the same width.  You can buy the strap without a buckle, or buy another belt long enough that you can cut off the buckle and insert the leather strap in this buckle.  One strategy is just to buy a cheap belt the right width, cut off the buckle and use the strap for as long as it lasts, then replace it again when it wears out.